Proportion and Scale Analysis Paper

Please read Chapter 6 : Proportion and Scale

ARCHITECTURE: Form, Space, & Order

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Define “proportion & scale”

Define and Elaborate on “Anthropometry” and “human scale”. Discuss what you found interesting about this chapter.

Initial Posts are Due on Sunday with Classmate engagements due on Tuesday at 11:59 PM.

Your posts in the discussion area should exhibit careful thought and logical reasoning and provide evidence for your position. Each post should be at least one well-developed paragraph (approximately 100 words or more). Use correct spelling, punctuation, and grammar. Please read and reply to the posts of at least two other students for each discussion. Your replies should offer new substantiated ideas or thoughtful questions.

Grade – Rubrics:

Proportion and Scale definition – 20 pts

Anthropometry definition – 20 pts

Human scale definition – 20 pts

Student exploration about “what you found interesting about this chapter”- 20 pts

Classmates replies – 20 pts

ISBN: 0-471-75216-9

Architecture/Reference C H I N G



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F R A N C I S D . K . C H I N G

F O R M , S P A C E , A N D O R D E R



A superb visual reference to the principles of architecture

Now including interactive CD-ROM!

F or more than thirty years, the beautifully illustrated Architecture: Form, Space,

and Order has been the classic introduction to the basic vocabulary of

architectural design. The updated Third Edition features expanded sections

on circulation, light, views, and site context, along with new considerations of

environmental factors, building codes, and contemporary examples of form, space,

and order.

This classic visual reference helps both students and practicing architects

understand the basic vocabulary of architectural design by examining how form

and space are ordered in the built environment. Using his trademark meticulous

drawing, Professor Ching shows the relationship between fundamental elements

of architecture through the ages and across cultural boundaries. By looking at these

seminal ideas, Architecture: Form, Space, and Order encourages the reader to look

critically at the built environment and promotes a more evocative understanding

of architecture.

In addition to updates to content and many of the illustrations, this new edition

includes a companion CD-ROM that brings the book’s architectural concepts to life

through three-dimensional models and animations created by Professor Ching.

FRANCIS D.K. CHING is the bestselling author of numerous books on architecture

and design, including A Global History of Architecture, Architectural Graphics, A

Visual Dictionary of Architecture, Interior Design Illustrated, and Building Construction

Illustrated, all published by Wiley. He is a registered architect and Professor Emeritus

at the University of Washington in Seattle.

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ARCHITECTURE Form, Space, & Order Third Edi t ion







ARCHITECTURE Form, Space, & Order Third Edi t ion

Francis D.K. Ching

John Wiley & Sons, Inc.



Library of Congress Cataloging-in-Publication Data:

Ching, Frank, 1943- Architecture–form, space, & order / Francis D.K. Ching. — 3rd ed. p. cm. Includes bibliographical references and index. ISBN 978-0-471-75216-5 (pbk.) 1. Architecture–Composition, proportion, etc. 2. Space (Architecture) I. Title. NA2760.C46 2007 720.1–dc22 2007002358

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Preface vii Introduction ix 1 Primary Elements Primary Elements 2 Point 4 Point Elements 5 Two Points 6 Line 8 Linear Elements 10 From Line to Plane 14 Plane 18 Planar Elements 20 Volume 28 Volumetric Elements 30 2 Form Properties of Form 35 Shape 36 Primary Shapes 38 Circle 39 Triangle 40 Square 41 Surfaces 42 Curved Surfaces 43 Primary Solids 44 Regular & Irregular forms 48 Transformation of Form 50 Dimensional Transformation 52 Subtractive Form 54 Subtractive & Additive Forms 57 Additive Form 58 Centralized Form 60 Linear Form 62 Radial Form 66 Clustered Form 68 Grid Form 72 Formal Collisions of Geometry 74 Circle & Square 76 Rotated Grid 78 Articulation of Form 80 Edges & Corners 82 Surface Articulation 88

3 Form & Space Form & Space: Unity of Opposites 96 Form Defining Space 102 Horizontal Elements Defining Space 103 Base Plane 104 Elevated Base Plane 106 Depressed Base Plane 112 Overhead Plane 118 Vertical Elements Defining Space 124 Vertical Linear Elements 126 Single Vertical Plane 134 L-Shaped Configuration of Planes 138 Parallel Vertical Planes 144 U-Shaped Planes 150 Four Planes: Closure 156 Summary Typology: Space-Defining Elements 160 Openings in Space-Defining Elements 162 Openings within Planes 164 Openings at Corners 166 Openings between Planes 168 Qualities of Architectural Space 170 Degree of Enclosure 172 Light 174 View 178 4 Organization Organization of Form & Space 184 Spatial Relationships 185 Space within a Space 186 Interlocking Spaces 188 Adjacent Spaces 190 Spaces Linked by a Common Space 192 Spatial Organizations 194 Centralized Organizations 196 Linear Organizations 206 Radial Organizations 216 Clustered Organizations 222 Grid Organizations 230





5 Circulation Circulation: Movement through Space 240 Circulation Elements 241 Approach 242 Entrance 250 Configuration of the Path 264 Path-Space Relationships 278 Form of the Circulation Space 282 6 Proportion & Scale Proportion & Scale 294 Material Proportions 295 Structural Proportions 296 Manufactured Proportions 298 Proportioning Systems 299 Golden Section 302 Regulating Lines 306 Classical Orders 308 Renaissance Theories 314 Modulor 318 Ken 322 Anthropometry 326 Scale 329 Visual Scale 330 Human Scale 332 A Scalar Comparison 334 7 Principles Ordering Principles 338 Axis 340 Symmetry 348 Hierarchy 358 Datum 366 Rhythm 382 Repetition 383 Transformation 402

Conclusion 406 A Selected Bibliography 409 Glossary 411 Index 419




The original edition of this study introduced the student of architecture to form and space and the principles that guide their ordering in the built environment. Form and space are the critical means of architecture that comprise a design vocabulary that is both elemental and timeless. The second edition continued to be a comprehensive primer on the ways form and space are interrelated and organized in the shaping of our environment, and was refined by editing the text and incorporating diagrams for greater clarity, adding selected examples of architectural works, expanding the sections on openings, stairways and scale, and finally, by including a glossary and an index to designers. This third edition continues to illustrate the ways the fundamental elements and principals of architectural design manifest themselves over the course of human history but adds an electronic component to introduce the aspects of time and movement to the exposition of elements and principles.

The historical models in this book span time and cross cultural boundaries. While the juxtaposition of styles may appear to be abrupt at times, the diverse range of examples is deliberate. The collage is intended to persuade the reader to look for likenesses among seemingly unlike constructions and bring into sharper focus the critical distinctions that reflect the time and place of their making. Readers are encouraged to take note of additional examples encountered or recalled within the context of their individual experiences. As the design elements and principles become more familiar, new connections, relationships, and levels of meaning may be established.

The illustrated examples are neither exhaustive nor necessarily the prototypes for the concepts and principles discussed. Their selection merely serves to illuminate and clarify the formal and spatial ideas being explored. These seminal ideas transcend their historical context and encourage speculation: How might they be analyzed, perceived, and experienced? How might they be transformed into coherent, useful, and meaningful structures of space and enclosure? How might they be reapplied to a range of architectural problems? This manner of presentation attempts to promote a more evocative understanding of the architecture one experiences, the architecture one encounters in literature, and the architecture one imagines while designing.







I am indebted to the following people for their invaluable contributions to the original edition of this work: Forrest Wilson, whose insights into the communication of design principles helped clarify the organization of the material, and whose support made its publication possible; James Tice, whose knowledge and understanding of architectural history and theory strengthened the development of this study; Norman Crowe, whose diligence and skill in the teaching of architecture encouraged me to pursue this work; Roger Sherwood, whose research into the organizational principles of form fostered the development of the chapter on ordering principles; Daniel Friedman, for his enthusiasm and careful editing of the final copy; Diane Turner and Philip Hamp, for their assistance in researching material for the illustrations; and to the editorial and production staff at Van Nostrand Reinhold, for their exceptional support and service during the making of the first edition.

For the second edition, my appreciation goes to the many students and their teachers who have used this book over the years and offered suggestions for its improvement as a reference and tool for study and teaching. I want to especially thank the following educators for their careful critique of the first edition: L. Rudolph Barton, Laurence A. Clement, Jr., Kevin Forseth, Simon Herbert, Jan Jennings, Marjorie Kriebel, Thomas E. Steinfeld, Cheryl Wagner, James M. Wehler, and Robert L. Wright.

In preparing this third edition, I am thankful to Michele Chiuini, Ahmeen Farooq, and Dexter Hulse for their thoughtful reviews of the second edition. While I have attempted to incorporate much of their wise counsel, I remain solely responsible for any deficiencies remaining in the text. I especially want to express my gratitude to the editorial and production staff at John Wiley & Sons for their invaluable support and encouragement, and to Nan-ching Tai for his creative contributions and technical assistance in preparing the electronic component of this third edition.


To Debra, Emily, and Andrew, whose love of life it is ultimately the role of architecture to house.




Architecture is generally conceived—designed—and realized—built—in response to an existing set of conditions. These conditions may be purely functional in nature, or they may also reflect in varying degrees the social, political, and economic climate. In any case, it is assumed that the existing set of conditions—the problem—is less than satisfactory and that a new set of conditions—a solution—would be desirable. The act of creating architecture, then, is a problem-solving or design process.

The initial phase of any design process is the recognition of a problematic condition and the decision to find a solution to it. Design is above all a willful act, a purposeful endeavor. A designer must first document the existing conditions of a problem, define its context, and collect relevant data to be assimilated and analyzed. This is the critical phase of the design process since the nature of a solution is inexorably related to how a problem is perceived, defined, and articulated. Piet Hein, the noted Danish poet and scientist, puts it this way: “Art is solving problems that cannot be formulated before they have been solved. The shaping of the question is part of the answer.”

Designers inevitably and instinctively prefigure solutions to the problems they are confronted with, but the depth and range of their design vocabulary influence both their perception of a question and the shaping of its answer. If one’s understanding of a design language is limited, then the range of possible solutions to a problem will also be limited. This book focuses, therefore, on broadening and enriching a vocabulary of design through the study of its essential elements and principles and the exploration of a wide array of solutions to architectural problems developed over the course of human history.

As an art, architecture is more than satisfying the purely functional requirements of a building program. Fundamentally, the physical manifestations of architecture accommodate human activity. However, the arrangement and ordering of forms and spaces also determine how architecture might promote endeavors, elicit responses, and communicate meaning. So while this study focuses on formal and spatial ideas, it is not intended to diminish the importance of the social, political, or economic aspects of architecture. Form and space are presented not as ends in themselves but as means to solve a problem in response to conditions of function, purpose, and context—that is, architecturally.

The analogy may be made that one must know and understand the alphabet before words can be formed and a vocabulary developed; one must understand the rules of grammar and syntax before sentences can be constructed; one must understand the principles of composition before essays, novels, and the like can be written. Once these elements are understood, one can write poignantly or with force, call for peace or incite to riot, comment on trivia or speak with insight and meaning. In a similar way, it might be appropriate to be able to recognize the basic elements of form and space and understand how they can be manipulated and organized in the development of a design concept, before addressing the more vital issue of meaning in architecture.







In order to place this study in proper context, the following is an overview of the basic elements, systems, and orders that constitute a work of architecture. All of these constituents can be perceived and experienced. Some may be readily apparent while others are more obscure to our intellect and senses. Some may dominate while others play a secondary role in a building’s organization. Some may convey images and meaning while others serve as qualifiers or modifiers of these messages.

In all cases, however, these elements and systems should be interrelated to form an integrated whole having a unifying or coherent structure. Architectural order is created when the organization of parts makes visible their relationships to each other and the structure as a whole. When these relationships are perceived as mutually reinforcing and contributing to the singular nature of the whole, then a conceptual order exists—an order that may well be more enduring than transient perceptual visions.

Architectural Systems


• organizational pattern, relationships, clarity, hierarchy • formal image and spatial definition • qualities of shape, color, texture, scale, proportion • qualities of surfaces, edges, and openings

• approach and entry • path configuration and access • sequence of spaces • light, view, touch, hearing, and smell

• structure and enclosure • environmental protection and comfort • health, safety, and welfare • durability and sustainability

• user requirements, needs, aspirations • sociocultural factors • economic factors • legal constraints • historical tradition and precedents

• site and environment • climate: sun, wind, temperature, precipitation • geography: soils, topography, vegetation, water • sensory and cultural characteristics of the place

The Architecture of Space Structure Enclosure

Experienced through Movement in Space-Time

Achieved by means of Technology

Accommodating a Program

Compatible with its Context






Systems and organizations of • space • structure • enclosure • machines

• approach and departure • entry and egress • movement through the order of spaces • functioning of and activities within spaces • qualities of light, color, texture, view, and sound

• images • patterns • signs • symbols

• context

…& Orders



Physical Form and Space • solids and voids • interior and exterior

Perceptual Sensory perception and recognition of the physical elements by experiencing them sequentially in time

Conceptual Comprehension of the ordered or disordered relationships among a building’s elements and systems, and responding to the meanings they evoke

* Technics refers to the theory, principles, or study of an art or a process.





Spatial System • The three-dimensional integration of program elements and spaces

accommodates the multiple functions and relationships of a house.

Villa Savoye, Poissy, east of Paris, 1923–31, Le Corbusier

Structural system • A grid of columns supports horizontal beams and slabs. • The cantilever acknowledges the direction of approach along the

longitudinal axis.

Enclosure system • Four exterior wall planes define a rectangular volume that contains

the program elements and spaces.

This graphic analysis illustrates the way architecture embodies the harmonious integration of interacting and interrelated parts into a complex and unified whole.





Circulation system • The stair and ramp penetrate and link the three levels, and heighten

the viewer’s perception of forms in space and light. • The curved form of the entrance foyer reflects the movement of

the automobile.

Context • A simple exterior form wraps around a complex interior organization

of forms and spaces. • Elevating the main floor provides a better view and avoids the humidity

of the ground. • A garden terrace distributes sunlight to the spaces gathered around it.

“Its severe, almost square exterior surrounds an intricate interior configura- tion glimpsed through openings and from protrusions above. . . . Its inside order accommodates the multiple functions of a house, domestic scale, and partial mystery inherent in a sense of privacy. Its outside order expresses the unity of the idea of house at an easy scale appropriate to the green field it dominated and possibly to the city it will one day be part of.”

Robert Venturi, Complexity and Contradiction in Architecture, 1966










1 Primary Elements “All pictorial form begins with the point that sets itself in motion… The point moves . . . and the line comes into being—the first dimension. If the line shifts to form a plane, we obtain a two-dimensional element. In the movement from plane to spaces, the clash of planes gives rise to body (three-dimensional) . . . A summary of the kinetic energies which move the point into a line, the line into a plane, and the plane into a spatial dimension.”

Paul Klee The Thinking Eye: The Notebooks of Paul Klee (English translation) 1961





This opening chapter presents the primary elements of form in the order of their growth from the point to a one-dimensional line, from the line to a two- dimensional plane, and from the plane to a three-dimensional volume. Each element is first considered as a conceptual element, then as a visual element in the vocabulary of architectural design.

As conceptual elements, the point, line, plane, and volume are not visible except to the mind’s eye. While they do not actually exist, we nevertheless feel their presence. We can sense a point at the meeting of two lines, a line marking the contour of a plane, a plane enclosing a volume, and the volume of an object that occupies space.

When made visible to the eye on paper or in three-dimensional space, these elements become form with characteristics of substance, shape, size, color, and texture. As we experience these forms in our environment, we should be able to perceive in their structure the existence of the primary elements of point, line, plane, and volume.






As the prime generator of form, the

Point indicates a position in space.

A point extended becomes a Line with properties of: • length • direction • position

A line extended becomes a Plane with properties of: • length and width • shape • surface • orientation • position

A plane extended becomes a Volume with properties of: • length, width, and depth • form and space • surface • orientation • position










A point marks a position in space. Conceptually, it has no length, width, or depth, and is therefore static, centralized, and directionless.

As the prime element in the vocabulary of form, a point can serve to mark:

• the two ends of a line • the intersection of two lines • the meeting of lines at the corner of a plane or volume • the center of a field

Although a point theoretically has neither shape nor form, it begins to make its presence felt when placed within a visual field. At the center of its environment, a point is stable and at rest, organizing surrounding elements about itself and dominating its field.

When the point is moved off-center, however, its field becomes more aggressive and begins to compete for visual supremacy. Visual tension is created between the point and its field.






A point has no dimension. To visibly mark a position in space or on the ground plane, a point must be projected vertically into a linear form, as a column, obelisk, or tower. Any such columnar element is seen in plan as a point and therefore retains the visual characteristics of a point. Other point-generated forms that share these same visual attributes are the: Piazza del Campidoglio, Rome, c. 1544, Michelangelo Buonarroti.

The equestrian statue of Marcus Aurelius marks the center of this urban space.

Mont S. Michel, France, 13th century and later. The pyramidal composition culminates in a spire that serves to establish this fortified monastery as a specific place in the landscape.

• cylinder Baptistery at Pisa, Italy, 1153–1265, Dioti Salvi

• circle Tholos of Polycleitos, Epidauros, Greece, c. 350 B.C.

• sphere Cenotaph for Sir Isaac Newton, Project, 1784, Étienne-Louis Boulée






Two points describe a line that connects them. Although the points give this line finite length, the line can also be considered a segment of an infinitely longer path.

Two points further suggest an axis perpendicular to the line they describe and about which they are symmetrical. Because this axis may be infinite in length, it can be at times more dominant than the described line.

In both cases, however, the described line and the perpendicular axis are optically more dominant than the infinite number of lines that may pass through each of the individual points.






Two points established in space by columnar elements or centralized forms can define an axis, an ordering device used throughout history to organize building forms and spaces.

The Mall, Washington, D.C., lies along the axis established by the Lincoln Memorial, the Washington Monument, and the United States Capitol building.

In plan, two points can denote a gateway signifying passage from one place to another. Extended vertically, the two points define both a plane of entry and an approach perpendicular to it.

Torii, Ise Shrine, Mie Prefecture, Japan, A.D. 690






A point extended becomes a line. Conceptually, a line has length, but no width or depth. Whereas a point is by nature static, a line, in describing the path of a point in motion, is capable of visually expressing direction, movement, and growth.

A line is a critical element in the formation of any visual construction.

It can serve to:

• join, link, support, surround, or intersect other visual elements

• describe the edges of and give shape to planes

• articulate the surfaces of planes







Although a line theoretically has only one dimension, it must have some degree of thickness to become visible. It is seen as a line simply because its length dominates its width. The character of a line, whether taut or limp, bold or tentative, graceful or ragged, is determined by our perception of its length–width ratio, its contour, and its degree of continuity.

Even the simple repetition of like or similar elements, if continuous enough, can be regarded as a line. This type of line has significant textural qualities.

The orientation of a line affects its role in a visual construction. While a vertical line can express a state of equilibrium with the force of gravity, symbolize the human condition, or mark a position in space, a horizontal line can represent stability, the ground plane, the horizon, or a body at rest.

An oblique line is a deviation from the vertical or horizontal.

It may be seen as a vertical line falling or a horizontal line rising. In either case, whether it is falling toward a point on the ground plane or rising to a place in the sky, it is dynamic and visually active in its unbalanced state.





Vertical linear elements, such as columns, obelisks, and towers, have been used throughout history to commemorate significant events and establish particular points in space.

Menhir, a prehistoric monument consisting of an upright megalith, usually standing alone but sometimes aligned with others.

Column of Marcus Aurelius, Piazza Colonna, Rome, A.D. 174. This cylindrical shaft commemorates the emperor’s victory over Germanic tribes north of the Danube.

Obelisk of Luxor, Place de la Concorde, Paris. The obelisk, which marked the entrance to the Amon temple at Luxor, was given by the viceroy of Egypt, Mohamed Ali, to Louis Phillipe and installed in 1836.

Bell Tower, Church at Vuoksenniska, Finland, 1956, Alvar Aalto

Vertical linear elements can also define a transparent volume of space. In the example illustrated to the left, four minaret towers outline a spatial field from which the dome of the Selim Mosque rises in splendor.

Selim Mosque, Edirne, Turkey, A.D. 1569–75






Linear members that possess the necessary material strength can perform structural functions. In these three examples, linear elements:

• express movement across space • provide support for an overhead plane • form a three-dimensional structural frame

for architectural space

Caryatid Porch, The Erechtheion, Athens, 421–405 B.C., Mnesicles. The sculptured female figures stand as columnar supports for the entablature.

Katsura Imperial Villa, Kyoto, Japan, 17th century. Linear columns and beams together form a three-dimensional framework for architectural space.

Salginatobel Bridge, Switzerland, 1929–30, Robert Maillart. Beams and girders have the bending strength to span the space between their supports and carry transverse loads.






A line can be an imagined element rather than a visible one in architecture. An example is the axis, a regulating line established by two distant points in space and about which elements are symmetrically arranged.

Although architectural space exists in three dimensions, it can be linear in form to accommodate the path of movement through a building and link its spaces to one another.

House 10, 1966, John Hejduk

Buildings also can be linear in form, particularly when they consist of repetitive spaces organized along a circulation path. As illustrated here, linear building forms have the ability to enclose exterior spaces as well as adapt to the environmental conditions of a site.

Cornell University Undergraduate Housing, Ithaca, New York, 1974, Richard Meier

Villa Aldobrandini, Italy, 1598–1603, Giacomo Della Porta






At a smaller scale, lines articulate the edges and surfaces of planes and volumes. These lines can be expressed by joints within or between building materials, by frames around window or door openings, or by a structural grid of columns and beams. How these linear elements affect the texture of a surface will depend on their visual weight, spacing, and direction.

Town Hall, Säynätsalo, Finland, 1950–52, Alvar Aalto

Crown Hall, School of Architecture and Urban Design, Illinois Institute of Technology, Chicago, 1956, Mies van der Rohe

Seagram Building, New York City, 1956–58, Mies van de Rohe and Philip Johnson






Two parallel lines have the ability to visually describe a plane. A transparent spatial membrane can be stretched between them to acknowledge their visual relationship. The closer these lines are to each other, the stronger will be the sense of plane they convey.

A series of parallel lines, through their repetitiveness, reinforces our perception of the plane they describe. As these lines extend themselves along the plane they describe, the implied plane becomes real and the original voids between the lines revert to being mere interruptions of the planar surface.

The diagrams illustrate the transformation of a row of round columns, initially supporting a portion of a wall, then evolving into square piers which are an integral part of the wall plane, and finally becoming pilasters—remnants of the original columns occurring as a relief along the surface of the wall.

“The column is a certain strengthened part of a wall, carried up perpendicular from the foundation to the top … A row of columns is indeed nothing but a wall, open and discontinued in several places.” Leon Battista Alberti






A row of columns supporting an entablature—a colonnade—is often used to define the public face or facade of a building, especially one that fronts on a major civic space. A colonnaded facade can be penetrated easily for entry, offers a degree of shelter from the elements, and forms a semi-transparent screen that unifies individual building forms behind it.

Stoa of Attalus fronting the Agora in Athens

Altes Museum, Berlin, 1823–30, Karl Friedrich von Schinkel

The Basilica, Vicenza, Italy. Andrea Palladio designed this two-story loggia in 1545 to wrap around an existing medieval structure. This addition not only buttressed the existing structure but also acted as a screen that disguised the irregularity of the original core and presented a uniform but elegant face to the Piazza del Signori.






In addition to the structural role columns play in supporting an overhead floor or roof plane, they can articulate the penetrable boundaries of spatial zones which mesh easily with adjacent spaces.

St. Philibert, Tournus, France, 950 –1120. This view of the nave shows how rows of columns can provide a rhythmic measure of space.

These two examples illustrate how columns can define the edges of an exterior space defined within the mass of a building as well as articulate the edges of a building mass in space.

Temple of Athena Polias, Priene, c. 334 B.C., Pythius

Cloister of Moissac Abbey, France, c. 1100






The linear members of trellises and pergolas can provide a moderate degree of definition and enclosure for outdoor spaces while allowing filtered sunlight and breezes to penetrate.

Vertical and horizontal linear elements together can define a volume of space such as the solarium illustrated to the right. Note that the form of the volume is determined solely by the configuration of the linear elements.

Cary House, Mill Valley, California, 1963, Joseph Esherick Trellised Courtyard, Georgia O’Keefe Residence, Abiquiu, northwest of Sante Fe, New Mexico


Solarium of Condominium Unit 1, Sea Ranch, California, 1966, MLTW





A line extended in a direction other than its intrinsic direction becomes a plane. Conceptually, a plane has length and width, but no depth.

Shape is the primary identifying characteristic of a plane. It is determined by the contour of the line forming the edges of a plane. Because our perception of shape can be distorted by perspective foreshortening, we see the true shape of a plane only when we view it frontally.

The supplementary properties of a plane—its surface color, pattern, and texture—affect its visual weight and stability.

In the composition of a visual construction, a plane serves to define the limits or boundaries of a volume. If architecture as a visual art deals specifically with the formation of three- dimensional volumes of mass and space, then the plane should be regarded as a key element in the vocabulary of architectural design.






Planes in architecture define three-dimensional volumes of mass and space. The properties of each plane—size, shape, color, texture —as well as their spatial relationship to one another ultimately determine the visual attributes of the form they define and the qualities of the space they enclose.

In architectural design, we manipulate three generic types of planes:

Overhead Plane The overhead plane can be either the roof plane that spans and shelters the interior spaces of a building from the climatic elements, or the ceiling plane that forms the upper enclosing surface of a room.

Wall Plane The wall plane, because of its vertical orientation, is active in our normal field of vision and vital to the shaping and enclosure of architectural space.

Base Plane The base plane can be either the ground plane that serves as the physical foundation and visual base for building forms, or the floor plane that forms the lower enclosing surface of a room upon which we walk.






The ground plane ultimately supports all architectural construction. Along with climate and other environmental conditions of a site, the topographical character of the ground plane influences the form of the building that rises from it. The building can merge with the ground plane, rest firmly on it, or be elevated above it.

The ground plane itself can be manipulated as well to establish a podium for a building form. It can be elevated to honor a sacred or significant place; bermed to define outdoor spaces or buffer against undesirable conditions; carved or terraced to provide a suitable platform on which to build; or stepped to allow changes in elevation to be easily traversed.

Scala de Spagna (Spanish Steps), Rome, 1721–25. Alessandro Specchi designed this civic project to connect the Piazza di Spagna with SS. Trinita de’ Monti; completed by Francesco de Sanctis.

Mortuary Temple of Queen Hatshepsut, Dêr el-Bahari, Thebes, 1511–1480 B.C., Senmut. Three terraces approached by ramps rise toward the base of the cliffs where the chief sanctuary is cut deep into the rock.

Machu Picchu, an ancient Incan city established c.1500 in the Andes Mountains on a saddle between two peaks, 8000 ft. above the Urubamba River in south-central Peru.






The floor plane is the horizontal element that sustains the force of gravity as we move around and place objects for our use on it. It may be a durable covering of the ground plane or a more artificial, elevated plane spanning the space between its supports. In either case, the texture and density of the flooring material influences both the acoustical quality of a space and how we feel as we walk across its surface.

While the pragmatic, supportive nature of the floor plane limits the extent to which it can be manipulated, it is nonetheless an important element of architectural design. Its shape, color, and pattern determine to what degree it defines spatial boundaries or serves as a unifying element for the different parts of a space.

Like the ground plane, the form of a floor plane can be stepped or terraced to break the scale of a space down to human dimensions and create platforms for sitting, viewing, or performing. It can be elevated to define a sacred or honorific place. It can be rendered as a neutral ground against which other elements in a space are seen as figures.

Sitting Area, Lawrence House, Sea Ranch, California, 1966, MLTW/ Moore-Turnbull

Bacardi Office Building, Santiago de Cuba, 1958, Mies van der Rohe

Emperor’s Seat, Imperial Palace, Kyoto, Japan, 17th century






Exterior wall planes isolate a portion of space to create a controlled interior environment. Their construction provides both privacy and protection from the climatic elements for the interior spaces of a building, while openings within or between their boundaries reestablish a connection with the exterior environ- ment. As exterior walls mold interior space, they simultaneously shape exterior space and describe the form, massing, and image of a building in space.

As a design element, the plane of an exterior wall can be articulated as the front or primary facade of a building. In urban situations, these facades serve as walls that define courtyards, streets, and such public gathering places as squares and marketplaces.

Uffizi Palace, 1560–65, Giorgio Vasari. This Florentine street defined by the two wings of the Uffizi Palace links the Piazza della Signoria with the River Arno.

Piazza of San Marco, Venice. The continuous facades of buildings form the “walls” of the urban space.

S. Maria Novella, Florence, 1456–70. The Renaissance facade by Alberti presents a public face to a square.






Peyrissac Residence, Cherchell, North Africa, 1942, Le Corbusier

In the project to the right, freestanding brick bearing walls, together with L-shaped and T-shaped configurations of planes, create an interlocking series of spaces.

A compelling way to use the vertical wall plane is as a supporting element in the bearing-wall structural system. When arranged in a parallel series to support an overhead floor or roof plane, bearing walls define linear slots of space with strong directional qualities. These spaces can be related to one another only by interrupting the bearing walls to create perpendicular zones of space.

Country House in Brick, Project, 1923, Mies van der Rohe






Interior wall planes govern the size and shape of the internal spaces or rooms within a building. Their visual properties, their relationship to one another, and the size and distribution of openings within their boundaries determine both the quality of the spaces they define and the degree to which adjoining spaces relate to one another.

As a design element, a wall plane can merge with the floor or ceiling plane, or be articulated as an element isolated from adjacent planes. It can be treated as a passive or receding backdrop for other elements in the space, or it can assert itself as a visually active element within a room by virtue of its form, color, texture, or material.

While walls provide privacy for interior spaces and serve as barriers that limit our movement, doorways and windows reestablish continuity with neighboring spaces and allow the passage of light, heat, and sound. As they increase in size, these openings begin to erode the natural sense of enclosure walls provide. Views seen through the openings become part of the spatial experience.

Concert Hall, Project, 1942, Mies van der Rohe

Finnish Pavilion, New York World’s Fair, 1939, Alvar Aalto






While we walk on a floor and have physical contact with walls, the ceiling plane is usually out of our reach and is almost always a purely visual event in a space. It may be the underside of an overhead floor or roof plane and express the form of its structure as it spans the space between its supports, or it may be suspended as the upper enclosing surface of a room or hall.

As a detached lining, the ceiling plane can symbolize the sky vault or be the primary sheltering element that unifies the different parts of a space. It can serve as a repository for frescoes and other means of artistic expression or be treated simply as a passive or receding surface. It can be raised or lowered to alter the scale of a space or to define spatial zones within a room. Its form can be manipulated to control the quality of light or sound within a space.

Hangar, Design I, 1935, Pier Luigi Nervi. The lamella structure expresses the way forces are resolved and channeled down to the roof supports.

Church at Vuoksenniska, Finland, 1956, Alvar Aalto. The form of the ceiling plane defines a progression of spaces and enhances their acoustical quality.

Brick House, New Canaan, Connecticut, 1949, Philip Johnson. The detached vaulted ceiling plane appears to float above the bed.






The roof plane is the essential sheltering element that protects the interior of a building from the climatic elements. The form and geometry of its structure is established by the manner in which it spans across space to bear on its supports and slopes to shed rain and melting snow. As a design element, the roof plane is significant because of the impact it can have on the form and silhouette of a building within its setting.

The roof plane can be hidden from view by the exterior walls of a building or merge with the walls to emphasize the volume of the building mass. It can be expressed as a single sheltering form that encompasses a variety of spaces beneath its canopy, or comprise a number of hats that articulate a series of spaces within a single building.

A roof plane can extend outward to form overhangs that shield door and window openings from sun or rain, or continue downward further still to relate itself more closely to the ground plane. In warm climates, it can be elevated to allow cooling breezes to flow across and through the interior spaces of a building.

Dolmen, a prehistoric monument consisting of two or more large upright stones supporting a horizontal stone slab, found especially in Britain and France and usually regarded as a burial place for an important person.

Robie House, Chicago,1909, Frank Lloyd Wright. The low sloping roof planes and broad overhangs are characteristic of the Prairie School of Architecture.

Shodhan House, Ahmedabad, India, 1956, Le Corbusier. A grid of columns elevates the reinforced concrete roof slab above the main volume of the house.






The overall form of a building can be endowed with a distinctly planar quality by carefully introducing openings that expose the edges of vertical and horizontal planes. These planes can be further differentiated and accentuated by changes in color, texture, or material.

Fallingwater (Kaufmann House), near Ohiopyle, Pennsylvania ,1936–37, Frank Lloyd Wright. Reinforced concrete slabs express the horizontality of the floor and roof planes as they cantilever outward from a central vertical core.

Schröder House, Utrecht, 1924–25, Gerrit Thomas Rietveld. Asymmetrical compositions of simple rectangular forms and primary colors characterized the de Stijl school of art and architecture.






A plane extended in a direction other than its intrinsic direction becomes a volume. Conceptually, a volume has three dimensions: length, width, and depth.

All volumes can be analyzed and understood to consist of: • points or vertices where several planes come together • lines or edges where two planes meet • planes or surfaces that define the limits or boundaries

of a volume

Form is the primary identifying characteristic of a volume. It is established by the shapes and interrelationships of the planes that describe the boundaries of the volume.

As the three-dimensional element in the vocabulary of architectural design, a volume can be either a solid— space displaced by mass—or a void—space contained or enclosed by planes.






Plan and Section Space defined by wall, floor, and ceiling or roof planes

In architecture, a volume can be seen to be either a portion of space contained and defined by wall, floor, and ceiling or roof planes, or a quantity of space displaced by the mass of a building. It is important to perceive this duality, especially when reading orthographic plans, elevations, and sections.

Notre Dame Du Haut, Ronchamp, France, 1950–55, Le Corbusier

Elevation Space displaced by the mass of a building






Building forms that stand as objects in the landscape can be read as occupying volumes in space.

Doric Temple at Segesta, Sicily, c. 424–416 B.C. Villa Garches, Vaucresson, France, 1926–27, Le Corbusier

Barn in Ontario, Canada






Buddhist Chaitya Hall at Karli, Maharashtra, India, A.D. 100–125. The sanctuary is a volume of space carved out of the mass of solid rock.

Palazzo Thiene, Vicenza, Italy, 1545, Andrea Palladio. The interior rooms surround a cortile— the principal courtyard of an Italian palazzo.

Piazza Maggiore, Sabbioneta, Italy. A series of buildings enclose an urban square.

Building forms that serve as containers can be read as masses that define volumes of space.









2 Form “Architectural form is the point of contact between mass and space … Architectural forms, textures, materials, modulation of light and shade, color, all combine to inject a quality or spirit that articulates space. The quality of the architecture will be determined by the skill of the designer in using and relating these elements, both in the interior spaces and in the spaces around buildings.”

Edmund N. Bacon The Design of Cities 1974





Form is an inclusive term that has several meanings. It may refer to an external appearance that can be recognized, as that of a chair or the human body that sits in it. It may also allude to a particular condition in which something acts or manifests itself, as when we speak of water in the form of ice or steam. In art and design, we often use the term to denote the formal structure of a work—the manner of arranging and coordinating the elements and parts of a composition so as to produce a coherent image.

In the context of this study, form suggests reference to both internal structure and external outline and the principle that gives unity to the whole. While form often includes a sense of three-dimensional mass or volume, shape refers more specifically to the essential aspect of form that governs its appearance—the configuration or relative disposition of the lines or contours that delimit a figure or form.

Shape The characteristic outline or surface configuration of a particular form. Shape is the principal aspect by which we identify and categorize forms.

In addition to shape, forms have visual properties of:

Size The physical dimensions of length, width, and depth of a form. While these dimensions determine the proportions of a form, its scale is determined by its size relative to other forms in its context.

Color A phenomenon of light and visual perception that may be described in terms of an individual’s perception of hue, saturation, and tonal value. Color is the attribute that most clearly distinguishes a form from its environ- ment. It also affects the visual weight of a form.

Texture The visual and especially tactile quality given to a surface by the size, shape, arrangement, and proportions of the parts. Texture also determines the degree to which the surfaces of a form reflect or absorb incident light.





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All of these properties of form are in reality affected by the conditions under which we view them.

• A changing perspective or angle of view presents different shapes or aspects of a form to our eyes. • Our distance from a form determines its apparent size. • The lighting conditions under which we view a form affects the clarity of its shape and structure. • The visual field surrounding a form influences our ability to read and identify it.


Forms also have relational properties that govern the pattern and composition of elements:

Position The location of a form relative to its environment or the visual field within which it is seen.

Orientation The direction of a form relative to the ground plane, the compass points, other forms, or to the person viewing the form.

Visual Inertia The degree of concentration and stability of a form. The visual inertia of a form depends on its geometry as well as its orientation relative to the ground plane, the pull of gravity, and our line of sight.





Bust of Queen Nefertiti The pattern of eye movement of a person viewing the figure, from research by Alfred L. Yarbus of the Institute for Problems of Information Transmission in Moscow.

Shape refers to the characteristic outline of a plane figure or the surface configuration of a volumetric form. It is the primary means by which we recognize, identify, and categorize particular figures and forms. Our perception of shape depends on the degree of visual contrast that exists along the contour separating a figure from its ground or between a form and its field.

In architecture, we are concerned with the shapes of:

• floor, wall, and ceiling planes that enclose space

• door and window openings within a spatial enclosure

• silhouettes and contours of building forms





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Central Pavilion, Horyu-Ji Temple, Nara, Japan, A.D. 607

These examples illustrate how shaping the juncture between mass and space expresses the manner in which the contours of a building mass rise from the ground plane and meet the sky.

Suleymaniye Mosque, Constantinople (Istanbul), 1551–58, Sinan


Villa Garches, Vaucresson, France, 1926–27, Le Corbusier. This architectural composition illustrates the interplay between the shapes of planar solids and voids.





Gestalt psychology affirms that the mind will simplify the visual environment in order to understand it. Given any composition of forms, we tend to reduce the subject matter in our visual field to the simplest and most regular shapes. The simpler and more regular a shape is, the easier it is to perceive and understand.

From geometry we know the regular shapes to be the circle, and the infinite series of regular polygons that can be inscribed within it. Of these, the most significant are the primary shapes: the circle, the triangle, and the square.

Circle A plane curve every point of which is equidistant from a fixed point within the curve

Triangle A plane figure bounded by three sides and having three angles

Square A plane figure having four equal sides and four right angles





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The circle is a centralized, introverted figure that is normally stable and self-centering in its environment. Placing a circle in the center of a field reinforces its inherent centrality. Associating it with straight or angular forms or placing an element along its circumference, however, can induce in the circle an apparent rotary motion.

Roman Theater according to Vitruvius

Compositions of circles and circular segments

Plan of the Ideal City of Sforzinda, 1464, Antonio Filarete

neutral stable unstable equilibrium


stable self-centered dynamic fixed in place





The triangle signifies stability. When resting on one of its sides, the triangle is an extremely stable figure. When tipped to stand on one of its vertices, however, it can either be balanced in a precarious state of equilibrium or be unstable and tend to fall over onto one of its sides.

Great Pyramid of Cheops at Giza, Egypt, c. 2500 B.C.

Modern Art Museum, Caracas, Venezuela, 1955, Oscar Niemeyer

Vigo Sundt House, Madison, Wisconsin, 1942, Frank Lloyd Wright





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The square represents the pure and the rational. It is a bilaterally symmetrical figure having two equal and perpendicular axes. All other rectangles can be considered variations of the square – deviations from the norm by the addition of height or width. Like the triangle, the square is stable when resting on one of its sides and dynamic when standing on one of its corners. When its diagonals are vertical and horizontal, however, the square exists in a balanced state of equilibrium.

Bathhouse, Jewish Community Center, Trenton, New Jersey, 1954–59, Louis Kahn

Compositions resulting from the rotation and modification of the square


Agora of Ephesus, Asia Minor, 3rd century B. C.





In the transition from the shapes of planes to the forms of volumes is situated the realm of surfaces. Surface first refers to any figure having only two dimensions, such as a flat plane. The term, however, can also allude to a curved two-dimensional locus of points defining the boundary of a three-dimensional solid. There is a special class of the latter that can be generated from the geometric family of curves and straight lines. This class of curved surfaces include the following:

• Cylindrical surfaces are generated by sliding a straight line along a plane curve, or vice versa. Depending on the curve, a cylindrical surface may be circular, elliptic, or parabolic. Because of its straight line geometry, a cylindrical surface can be regarded as being either a translational or a ruled surface.

• Translational surfaces are generated by sliding a plane curve along a straight line or over another plane curve.

• Ruled surfaces are generated by the motion of a straight line. Because of its straight line geometry, a ruled surface is generally easier to form and construct than a rotational or translational surface.

• Rotational surfaces are generated by rotating a plane curve about an axis.

• Paraboloids are surfaces all of whose intersections by planes are either parabolas and ellipses or parabolas and hyperbolas. Parabolas are plane curves generated by a moving point that remains equidistant from a fixed line and a fixed point not on the line. Hyperbolas are plane curves formed by the intersection of a right circular cone with a plane that cuts both halves of the cone.

• Hyperbolic paraboloids are surfaces generated by sliding a parabola with downward curvature along a parabola with upward curvature, or by sliding a straight line segment with its ends on two skew lines. It can thus be considered to be both a translational and a ruled surface.





FORM / 43


Walt Disney Concert Hall, Los Angeles, California, 1987–2003, Frank O. Gehry & Partners

Saddle surfaces have an upward curvature in one direction and a downward curvature in the perpendicular direction. Regions of downward curvature exhibit archlike action while regions of upward curvature behave as a cable structure. If the edges of a saddle surface are not supported, beam behavior may also be present.

The geometric basis for these curved surfaces can be effectively utilized in digital modeling as well as in the description, fabrication and assembly of curvilinear architectural elements and components. The fluid quality of curved surfaces contrasts with the angular nature of rectilinear forms and are appropriate for describing the form of shell structures as well as nonloadbearing elements of enclosure.

Symmetrical curved surfaces, such as domes and barrel vaults, are inherently stable. Asymetrical curved surfaces, on the other hand, can be more vigorous and expressive in nature. Their shapes change dramatically as we view them from different perspectives.





The primary shapes can be extended or rotated to generate volumetric forms or solids that are distinct, regular, and easily recognizable. Circles generate spheres and cylinders; triangles generate cones and pyramids; squares generate cubes. In this context, the term solid does not refer to firmness of substance but rather to a three-dimensional geometric body or figure.

“…cubes, cones, spheres, cylinders, or pyramids are the great primary forms that light reveals to advantage; the image of these is distinct and tangible within us and without ambiguity. It is for this reason that these are beautiful forms, the most beautiful forms.” Le Corbusier

Sphere A solid generated by the revolution of a semicircle about its diameter, whose surface is at all points equidistant from the center. A sphere is a centralized and highly concentrated form. Like the circle from which it is generated, it is self-centering and normally stable in its environment. It can be inclined toward a rotary motion when placed on a sloping plane. From any viewpoint, it retains its circular shape.

Cylinder A solid generated by the revolution of a rectangle about one of its sides. A cylinder is centralized about the axis passing through the centers of its two circular faces. Along this axis, it can be easily extended. The cylinder is stable if it rests on one of its circular faces; it becomes unstable when its central axis is inclined from the vertical.





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Cone A solid generated by the revolution of a right triangle about one of its sides. Like the cylinder, the cone is a highly stable form when resting on its circular base, and unstable when its vertical axis is tipped or overturned. It can also rest on its apex in a precarious state of balance.

Pyramid A polyhedron having a polygonal base and triangular faces meeting at a common point or vertex. The pyramid has properties similar to those of the cone. Because all of its surfaces are flat planes, however, the pyramid can rest in a stable manner on any of its faces. While the cone is a soft form, the pyramid is relatively hard and angular.

Cube A prismatic solid bounded by six equal square sides, the angle between any two adjacent faces being a right angle. Because of the equality of its dimensions, the cube is a static form that lacks apparent movement or direction. It is a stable form except when it stands on one of its edges or corners. Even though its angular profile is affected by our point of view, the cube remains a highly recognizable form.






Maupertius, Project for an Agricultural Lodge, 1775, Claude-Nicolas Ledoux

Project for a Conical Cenotaph, 1784, Étienne-Louis Boulée

Chapel, Massachusetts Institute of Technology, Cambridge, Massachusetts, 1955, Eero Saarinen and Associates





FORM / 47

Pyramids of Cheops, Chephren, and Mykerinos at Giza, Egypt, c. 2500 B.C.

Hanselmann House, Fort Wayne, Indiana, 1967, Michael Graves


Diwan-i-Khas, Fatehpur Sikri, Palace Complex of Akbar the Great Mogul Emperor of India, 1569–74





Regular forms refer to those whose parts are related to one another in a consistent and orderly manner. They are generally stable in nature and symmetrical about one or more axes. The sphere, cylinder, cone, cube, and pyramid are prime examples of regular forms.

Forms can retain their regularity even when transformed dimensionally or by the addition or subtraction of elements. From our experiences with similar forms, we can construct a mental model of the original whole even when a fragment is missing or another part is added.

Irregular forms are those whose parts are dissimilar in nature and related to one another in an inconsistent manner. They are generally asymmetrical and more dynamic than regular forms. They can be regular forms from which irregular elements have been subtracted or result from an irregular composition of regular forms.

Since we deal with both solid masses and spatial voids in architecture, regular forms can be con- tained within irregular forms. In a similar manner, irregular forms can be enclosed by regular forms.





FORM / 49

Irregular Forms: Philharmonic Hall, Berlin, 1956–63, Hans Scharoun

An Irregular Composition of Regular Forms: Katsura Imperial Villa, Kyoto, Japan, 17th century

A Regular Composition of Regular Forms: Coonley Playhouse, Riverside, Illinois, 1912, Frank Lloyd Wright

Irregular Forms within a Regular Field: Courtyard House Project, 1934, Mies van de Rohe

Regular Forms within an Irregular Composition: Mosque of Sultan Hasan, Cairo, Egypt, 1356–63






All other forms can be understood to be transformations of the primary solids, variations which are generated by the manipulation of one or more dimensions or by the addition or subtraction of elements.

Dimensional Transformation A form can be transformed by altering one or more of its dimensions and still retain its identity as a member of a family of forms. A cube, for example, can be transformed into similar prismatic forms through discrete changes in height, width, or length. It can be compressed into a planar form or be stretched out into a linear one.

Subtractive Transformation A form can be transformed by subtracting a portion of its volume. Depending on the extent of the subtractive process, the form can retain its initial identity or be transformed into a form of another family. For example, a cube can retain its identity as a cube even though a portion of it is removed, or be transformed into a series of regular polyhedrons that begin to approximate a sphere.

Additive Transformation A form can be transformed by the addition of elements to its volume. The nature of the additive process and the number and relative sizes of the elements being attached determine whether the identity of the initial form is altered or retained.





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Dimensional Transformation of a Cube into a Vertical Slab: Unité d’Habitation, Firminy-Vert, France, 1963–68, Le Corbusier

Subtractive Transformation Creating Volumes of Space: Gwathmey Residence, Amagensett, New York, 1967, Charles Gwathmey/Gwathmey Siegel

Additive Transformation of a Parent Form by the Attachment of Subordinate Parts: Il Redentore, Venice, 1577–92, Andrea Palladio






A sphere can be transformed into any number of ovoid or ellipsoidal forms by elongating it along an axis.

A pyramid can be transformed by altering the dimensions of the base, modifying the height of the apex, or tilting the normally vertical axis.

A cube can be transformed into similar prismatic forms by shortening or elongating its height, width, or depth.





FORM / 53

Plan of an Elliptical Church, Pensiero Della Chiesa S. Carlo, Project, 17th century, Francesco Borromini

St. Pierre, Firminy-Vert, France, 1965, Le Corbusier

Project for Yahara Boat Club, Madison, Wisconsin, 1902, Frank Lloyd Wright







We search for regularity and continuity in the forms we see within our field of vision. If any of the primary solids is partially hidden from our view, we tend to complete its form and visualize it as if it were whole because the mind fills in what the eyes do not see. In a similar manner, when regular forms have fragments missing from their volumes, they retain their formal identities if we perceive them as incomplete wholes. We refer to these mutilated forms as subtractive forms.

Because they are easily recognizable, simple geometric forms, such as the primary solids, adapt readily to subtractive treatment. These forms will retain their formal identities if portions of their volumes are removed without deteriorating their edges, corners, and overall profile.

Ambiguity regarding the original identity of a form will result if the portion removed from its volume erodes its edges and drastically alters its profile.

In the series of figures below, at what point does the square shape with a corner portion removed become an L- shaped configuration of two rectangular planes?




FORM / 55

Spatial volumes may be subtracted from a form to create recessed entrances, positive courtyard spaces, or window openings shaded by the vertical and horizontal surfaces of the recess.

Gorman Residence, Amagansett, New York, 1968, Julian and Barbara Neski

House at Stabio, Switzerland, 1981, Mario Botta


Khasneh al Faroun, Petra, 1st century A.D.





Shodhan House, Ahmedabad, India, 1956, Le Corbusier

Benacerraf House Addition, Princeton, New Jersey, 1969, Michael Graves


Gwathmey Residence, Amagansett, New York, 1967, Charles Gwathmey/Gwathmey Siegel & Associates




FORM / 57

Le Corbusier comments on form:

“Cumulative Composition • additive form • a rather easy type • picturesque; full of movement • can be completely disciplined by classification and


“Cubic Compositions (Pure Prisms) • very difficult (to satisfy the spirit)”

“very easy • (convenient combining)”

“subtractive form • very generous • on the exterior an architectural will is confirmed • on the interior all functional needs are satisfied (light

penetration, continuity, circulation)”

After a sketch, Four House Forms, by Le Corbusier for the cover of Volume Two of the Oeuvre Complète, published in 1935.

La Roche-Jeanneret Houses, Paris

Villa at Garches

House at Stuttgart

House at Poissy






While a subtractive form results from the removal of a portion of its original volume, an additive form is produced by relating or physically attaching one or more subordinate forms to its volume.

The basic possibilities for grouping two or more forms are by:

Interlocking Volumes In this type of relationship, the forms interpenetrate each other’s space. The forms need not share any visual traits.

Face-to-face Contact This type of relationship requires that the two forms have corresponding planar surfaces which are parallel to each other.

Edge-to-edge Contact In this type of relationship, the forms share a common edge and can pivot about that edge.

Spatial Tension This type of relationship relies on the close proximity of the forms or their sharing of a common visual trait, such as shape, color, or material.





FORM / 59

Additive forms resulting from the accretion of discrete elements can be characterized by their ability to grow and merge with other forms. For us to perceive additive groupings as unified compositions of form—as figures in our visual field—the combining elements must be related to one another in a coherent manner.

These diagrams categorize additive forms according to the nature of the relationships that exist among the component forms as well as their overall configurations. This outline of formal organizations should be compared with a parallel discussion of spatial organizations in Chapter 4.

Centralized Form A number of secondary forms clustered about a dominant, central parent-form

Linear Form A series of forms arranged sequentially in a row

Radial Form A composition of linear forms extending outward from a central form in a radial manner

Clustered Form A collection of forms grouped together by proximity or the sharing of a common visual trait

Grid Form A set of modular forms related and regulated by a three-dimensional grid


Lingaraja Temple, Bhubaneshwar, India, c. A.D. 1100





Villa Capra (The Rotunda), Vicenza, Italy, 1552–67, Andrea PalladioBeth Sholom Synagogue, Elkins Park, Pennsylvania, 1959, Frank Lloyd Wright

S. Maria Della Salute, Venice, 1631–82, Baldassare Longhena





FORM / 61

Centralized forms require the visual dominance of a geometrically regular, centrally located form, such as a sphere, cone, or cylinder. Because of their inherent centrality, these forms share the self-centering properties of the point and circle. They are ideal as freestanding structures isolated within their context, dominating a point in space, or occupying the center of a defined field. They can embody sacred or honorific places, or commemorate significant persons or events.

Yume-Dono, Eastern precinct of Horyu-Ji Temple, Nara, Japan, A.D. 607

Tempietto, S. Pietro in Montorio, Rome, 1502, Donato Bramante






A linear form can result from a proportional change in a form’s dimensions or the arrangement of a series of discrete forms along a line. In the latter case, the series of forms may be either repetitive or dissimilar in nature and organized by a separate and distinct element such as a wall or path.

• A linear form can be segmented or curvilinear to respond to topography, vegetation, views, or other features of a site.

• A linear form can front on or define an edge of an exterior space, or define a plane of entry into the spaces behind it.

• A linear form can be manipulated to enclose a portion of space.

• A linear form can be oriented vertically as a tower element to establish or denote a point in space.

• A linear form can serve as an organizing element to which a variety of secondary forms are attached.





FORM / 63

Runcorn New Town Housing, England,1967, James Stirling

Linear Growth through the Repetition of Forms

Linear Form Expressing Procession or Movement

Burroughs Adding Machine Company, Plymouth, Michigan, 1904, Albert Kahn






Linear Forms Fronting on or Defining Exterior Space

Agora of Assos, Asia Minor, 2nd Century B.C.

18th-century buildings fronting a tree-lined canal in Kampen, HollandQueen’s College, Cambridge, England, 1709–38, Nicholas Hawksmoor





FORM / 65

Linear Organizations of Space

Henry Babson House, Riverside, Illinois, 1907, Louis Sullivan

The Mile-high Illinois, Skyscraper Project, Chicago, Illinois, 1956, Frank Lloyd Wright






The core is either the symbolic or functional center of the organization. Its central position can be articulated with a visually dominant form, or it can merge with and become subservient to the radiating arms.

The radiating arms, having properties similar to those of linear forms, give a radial form its extroverted nature. They can reach out and relate to or attach themselves to specific features of a site. They can expose their elongated surfaces to desirable conditions of sun, wind, view, or space.

Radial forms can grow into a network of centers linked by linear arms.


A radial form consists of linear forms that extend outward from a centrally located core element in a radiating manner. It combines the aspects of centrality and linearity into a single composition.




FORM / 67

The organization of a radial form can best be seen and understood from an aerial viewpoint. When viewed from ground level, its central core element may not be clearly visible and the radiating pattern of its linear arms may be obscured or distorted through perspective foreshortening.

Skyscraper by the Sea, Project for Algiers, 1938, Le Corbusier

Secretariat Building, UNESCO Headquarters, Place de Fontenoy, Paris, 1953–58, Marcel Breuer

Ground-level view

Aerial view






While a centralized organization has a strong geometric basis for the ordering of its forms, a clustered organization groups its forms according to functional requirements of size, shape, or proximity. While it lacks the geometric regularity and intro- verted nature of centralized forms, a clustered organization is flexible enough to incorporate forms of various shapes, sizes, and orientations into its structure.

Considering their flexibility, clustered organizations of forms may be organized in the following ways:

• They can be attached as appendages to a larger parent form or space.

• They can be related by proximity alone to articulate and express their volumes as individual entities.

• They can interlock their volumes and merge into a single form having a variety of faces.

A clustered organization can also consist of forms that are generally equivalent in size, shape, and function. These forms are visually ordered into a coherent, nonhierarchical organi- zation not only by their close proximity to one another, but also by the similarity of their visual properties.





FORM / 69

A Cluster of Articulated Forms: House Study, 1956, James Stirling & James Gowan

A Cluster of Interlocking Forms: G.N. Black House (Kragsyde), Manchester-by-the Sea, Massachusetts, 1882–83, Peabody & Stearns

A Cluster of Forms Attached to a Parent Form: Vacation House, Sea Ranch, California, 1968, MLTW/Moore & Turnbull






Trulli Village, Alberobello, Italy Traditional dry-stone shelters in existence since the 17th century.


Taos Pueblo, New Mexico, 13th centuryDogon Housing Cluster, Southeastern Mali, West Africa, 15th century–present

Numerous examples of clustered housing forms can be found in the vernacular architecture of various cultures. Even though each culture produced a unique style in response to differing technical, climatic, and sociocultural factors, these clustered housing organizations usually maintained the individuality of each unit and a moderate degree of diversity within the context of an ordered whole.




FORM / 71

Habitat Israel, Jerusalem, 1969, Moshe Safdie

Vernacular examples of clustered forms can be readily transformed into modular, geometrically ordered compositions which are related to grid organizations of form.


Habitat Montreal, 1967, Moshe Safdie

Ggantija temple complex, Malta, c. 3000 B.C.





A grid is a system of two or more intersecting sets of regularly spaced parallel lines. It generates a geometric pattern of regularly spaced points at the intersections of the grid lines and regularly shaped fields defined by the grid lines themselves.

The most common grid is based on the geometry of the square. Because of the equality of its dimensions and its bilateral sym- metry, a square grid is essentially nonhierarchical and bidirec- tional. It can be used to break the scale of a surface down into measurable units and give it an even texture. It can be used to wrap several surfaces of a form and unify them with its repeti- tive and pervasive geometry.

The square grid, when projected into the third dimension, generates a spatial network of reference points and lines. Within this modular framework, any number of forms and spaces can be visually organized.

Conceptual Diagram, Gunma Prefectural Museum of Fine Arts, Japan, 1974, Arata Isozaki

Nakagin Capsule Building, Tokyo, 1972, Kisho Kurokawa





FORM / 73

Hattenbach Residence, Santa Monica, California, 1971–73, Raymond Kappe

Cubic Volumes

Structural Frame

Frame with Adjacent Spaces






Circle and Square Rotated Grid

When two forms differing in geometry or orientation collide and interpenetrate each other’s boundaries, each will vie for visual supremacy and dominance. In these situations, the following forms can evolve:

• The two forms can subvert their individual identities and merge to create a new composite form.

• One of the two forms can receive the other totally within its volume.

• The two forms can retain their individual identities and share the interlocking portion of their volumes.

• The two forms can separate and be linked by a third element that recalls the geometry of one of the original forms.





FORM / 75

Forms differing in geometry or orientation may be incorporated into a single organization for any of the following reasons:

• To accommodate or accentuate the differing requirements of interior space and exterior form

• To express the functional or symbolic importance of a form or space within its context

• To generate a composite form that incorporates the contrasting geometries into its centralized organization

• To inflect a space toward a specific feature of a building site

• To carve a well-defined volume of space from a building form

• To express and articulate the various construc- tional or mechanical systems that exist within a building form

• To reinforce a local condition of symmetry in a building form

• To respond to contrasting geometries of the topography, vegetation, boundaries, or existing structures of a site

• To acknowledge an already existing path of movement through a building site






Plan for an Ideal City, 1615, Vincenzo Scamozzi

The Island Villa (Teatro Marittimo), Hadrian’s Villa, Tivoli, Italy, A.D. 118–125


Chancellery Building, French Embassy, Brasilia, 1964–65, Le Corbusier

A circular form can be freestanding in its context to express its ideal shape and still incorporate a more functional, rectilinear geometry within its boundaries.

The centrality of a circular form enables it to act as a hub and unify forms of contrasting geometry or orientation about itself.




FORM / 77

Murray House, Cambridge, Massachusetts, 1969, MLTW/Moore-Turnbull


A circular or cylindrical space can serve to organize the spaces within a rectangular enclosure.

Museum for North Rhine–Westphalia, Dusseldorf, Germany, 1975, James Stirling & Michael Wilford

Lister County Courthouse, Solvesborg, Sweden, 1917–21, Gunnar Asplund





Plan of the Ideal City of Sforzinda, 1464, Antonio Filarete

St. Mark’s Tower, Project, New York City, 1929, Frank Lloyd Wright


Pearl Mosque, within the Red Fort, an imperial palace at Agra, India, 1658–1707. The interior space of this mosque is oriented exactly with the cardinal points so that the quibla wall faces in the direction of the holy city of Mecca, while its exterior conforms to the existing layout of the fort.




FORM / 79

Diagram as Architecture: House III for Robert Miller, Lakeville, Connecticut, 1971, Design Development Drawings, Peter Eisenman


A Diagram of Architecture: Taliesin West, near Scottsdale, Arizona, 1938–59, Frank Lloyd Wright

A diagram by Bernhard Hoesli of the geometry regulating the layout of Taliesin West

National Museum of Roman Art, Mérida, Spain, 1980–6, Rafael Moneo. The structural grid of the lower level of the museum floats over and contrasts with the geometry of the ancient Roman remains of Mérida.





Palacio Güell, Barcelona, 1885–89, Antonio Gaudi





FORM / 81

Articulation refers to the manner in which the surfaces of a form come together to define its shape and volume. An articulated form clearly reveals the precise nature of its parts and their relationships to each other and to the whole. Its surfaces appear as discrete planes with distinct shapes and their overall configuration is legible and easily perceived. In a similar manner, an articulated group of forms accentuates the joints between the constituent parts in order to visually express their individuality.

A form can be articulated by:

• differentiating adjoining planes with a change in material, color, texture, or pattern

• developing corners as distinct linear elements independent of the abutting planes

• removing corners to physically separate neighboring planes • lighting the form to create sharp contrasts in tonal value along edges

and corners

In opposition to the emphasis on joints and joinery, the corners of a form can be rounded and smoothed over to emphasize the continuity of its surfaces. Or a material, color, texture, or pattern can be carried across a corner onto the adjoining surfaces to de-emphasize the individuality of the surface planes and emphasize instead the volume of a form.






Since the articulation of a form depends to a great degree on how its surfaces meet each other at corners, how these edge conditions are resolved is critical to the definition and clarity of a form.

While a corner can be articulated by simply contrasting the surface qualities of the adjoining planes, or obscured by layering their joining with an optical pattern, our perception of its existence is also affected by the laws of perspective and the quality of light that illuminates the form.

For a corner to be formally active, there must be more than a slight deviation in the angle between the adjoining planes. Since we constantly search for regularity and continuity within our field of vision, we tend to regularize or smooth out slight irregularities in the forms we see. For example, a wall plane that is bent only slightly will appear to be a single flat plane, perhaps with a surface imperfection. A corner would not be perceived.

At what point do these formal deviations become an acute angle? . . . a right angle?

a segmented line? . . . a straight line?

a circular segment? . . . a change in a line’s contour?





FORM / 83

Corners define the meeting of two planes. If the two planes simply touch and the corner remains unadorned, the presence of the corner will depend on the visual treatment of the adjoining surfaces. This corner condition emphasizes the volume of a form.

A corner condition can be visually reinforced by introducing a separate and distinct element that is independent of the surfaces it joins. This element articulates the corner as a linear condition, defines the edges of the adjoining planes, and becomes a positive feature of the form.

If an opening is introduced to one side of the corner, one of the planes will appear to bypass the other. The opening diminishes the corner condition, weakens the definition of the volume within the form, and emphasizes the planar qualities of the neighboring surfaces.

If neither plane is extended to define the corner, a volume of space is created to replace the corner. This corner condition deteriorates the volume of the form, allows the interior space to leak outward, and clearly reveals the surfaces as planes in space.

Rounding off the corner emphasizes the continuity of the bounding surfaces of a form, the compactness of its volume, and softness of its contour. The scale of the radius of curvature is important. If too small, it becomes visually insignificant; if too large, it affects the interior space it encloses and the exterior form it describes.

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