Symmetry and Subsymmetry as Characteristics of Form-Making ...d-lab.kr/prof/2004_01.pdf · elevation even were they all cast in the same mould. A succession ofbuildings of any given

Journal of Architectural and Planning Research21: 1 (Spring, 2004) 24

SYMMETRY AND SUBSYMMETRY AS CHARACTERISTICS OFFORM-MAKING: THE SCHINDLER SHELTER

PROJECT OF 1933-1942

Jin-HoPark

This research introduces a formal methodology with an emphasis on the point group symmetry andsubsymmetry in the analysis and synthesis of architectural designs. Mathematical techniques,including spatial transformations, a lattice of subsymmetries, and a multiplication table, are reviewedas aformative principle of spatial compositions. The principle is applied to analyze R. M Schindler sunexecuted work, the Schindler Shelter of 1933-1942, which demonstrates systematicalexperimentation with symmetric transformations to generate design variations. The principle is alsoemployed to test the compositional possibilities of arranging a shelter on a city block to maximizestreetscape variety.

Copyright © 2004, Locke Science Publishing Company, Inc.Chicago, IL, USA All Rights Reserved

Journal of Architectural and Planning Research

21:1 (Spring, 2004) 2S

INTRODUCTION

The principle of symmetry prevails in architecture as a design strategy, or compositional methodol-

ogy, for form-making. It applies to a form as a whole, but it may also apply to components (not

necessarily discrete), which make up the form (Weyl, 1952; Rosen, 1975; March and Steadman,

1971; March, 1979; Hargittai, 1986, 1989; Griinbaum and Shephard, 1987; Emmer, 1993). Symme-

try also applies to the consequences of multiplying the form in some larger assembly, such as the

"room, building, city" analogy used by Alberti in the 15th century with regard to architectural design

(Alberti, 1988). Although the final designs may seem asymmetrical as a whole, several layers of

symmetry could be manifested in parts ofthe design, though not immediately recognizable even with

a keen eye for symmetry (Park, 2001).

The architect R. M. Schindler (1887-1953) provided an example of form-making that consciously

exploited symmetry to generate both interior room variations and multiple house orientations within

city blocks. A prime example of this symmetry is the Schindler Shelter project. Itwas used to illustratethe potential for the conscious application of symmetry in form-making. In particular, it showed how

variety might be produced as an outcome of using a unified formative principle. In the same volume,

Frank Lloyd Wright and Schindler had independently presented schemes for city residential land

development for Chicago in 1914 (Yeomans, 1915). Wright introduced his "quadruple block plan," or

group of four houses. Wright described the proposal as it impacts each householder:

His building is an unconscious but necessary grouping with three of his neighbors', looking out

upon harmonious groups of other neighbors, no two of which would present to him the same

elevation even were they all cast in the same mould. A succession ofbuildings of any given length

by this arrangement presents the aspect of a well-grouped buildings in a park, of greater

picturesque variety than is possible where facade follows facade.

(Yeomans, 1915 :96-1 02)

Two years later, as Wright left for Tokyo to work on the Imperial Hotel commission, he wrote a note

introducing "Mr. Schindler ... who will have charge of my affairs during my absence" (Sheine,

2001:29).

This study first presents a formal discussion of the mathematical structure of symmetry groups. Then,

an analysis is done of symmetry groups in the organization of individual shelter plans as characteris-

tics of form-making. Finally, compositional possibilities of arranging shelters on a city block are

demonstrated.

FORMAL DISCUSSION

Because of the potential obscurity of symmetry nested in asymmetrical design, a formal methodology

clearly accounting for different hierarchical levels of symmetric employment in architectural designs

is needed. In an effort to provide this methodology, a technique founded on the algebraic structure of

symmetry groups of a regular polygon in mathematics is presented in this paper (Grossman and

Magnus, 1964; March and Steadman, 1971; Budden, 1972; Lockwood and Macmillan, 1978; Martin,

1982; Coxeter, 1986). The methodology will provide not only the description of symmetrical struc-

tures of a design but also further insight on generating new designs by combining various symmetries.

Spatial Transformations

Symmetries in this paper are defined as spatial transformations that leave an object in a congruent

figure without changing its appearance as a whole. Spatial transformations are called isometries

when the transformations preserve the distances between points and angles. There are four kinds of

planar transformations: translations, rotations, reflections, and glide reflections (the composite

movement of reflections and translations). The set of all isometries of a figure forms a mathematical

Journal of Architectural and Planning Research21: I (Spring, 2004) 26

structure known as the symmetrygroup of the figure. It is throughthe study of these symmetry groupsthat different types of architecturaldesigns are clearly distinguishedwith regard to symmetry.

In two dimensions, there are twosymmetry groups of plane symme-try: the finite group and the infinitegroup. The finite group of planesymmetry is called the point group.Spatial transformations take placein a fixed point or line. The trans-formations involve rotation aboutthe point and reflection along thelines, or the combination of both.In the point symmetry group, notranslation takes place. Tn the infi-nite symmetry group, spatial trans-formations occur where the basicmovement is either a translation ora gl ide reflection. In this group,designs that are invariant underone directional translation arecalled the frieze group, and designsunder two directional translationsare called the wallpaper group.This paper deals with the symme-tries of the point groups in two di-mensions only.

r qlr

In two dimensions, there are twofinite point groups: the dihedralgroup denoted by Dn for some inte-ger n; and the cyclic group denotedby Cn' The spatial transformationsof the dihedral group comprise ro-tation and mirror reflection. Thecyclic group contains transforma-tions by rotation only. The point groups have no translation. The number of elements in a finite groupis called its order. The symmetry group ofDn has order 2n elements, while Cn has order n elements.For instance, the symmetry of the square, which is the dihedral group D4 of order 8, has eight distin-guishable spatial transformations that define it: four quarter-turns and four reflections - one eachabout the horizontal and vertical axes and the leading and trailing diagonal axes. C4 has four spatialtransformations: the four quarter-turns.

FIGURE 1. Eight distinguishable transformations of the square where "q"represents a quarter-turn clockwise rotation and "r" represents a mirror

reflection.

Valid operations of a symmetry group of the square include rotation about its center through 90, 180,270, or 360 degrees, and reflection on its four axes. Eight distinguishable transformations of thesymmetry group are labeled as I, q, q2, q3, r, qr, q2r, and q3r. In our notations, "I" denotes identity; "q"denotes a quarter-turn clockwise rotation of the square; "q2" denotes a half-turn clockwise rotation ofthe square; and "r" denotes a mirror reflection of the figure. The diagrams in Figure 1 illustrate theexact positions of the figure. Since there cannot be any more than 8 symmetries, each symmetryshould determine exactly one position for each corner.

••••

••

FIGURE 2. Lattice showing the order of sub symmetries from the completesymmetry of the square at the top and the asymmetrical identity at the bottom.


21: 1 (Spring, 2004) 27

Lattice of Subsymmetries of theSquare

Subsymmetries arise from a cur-

tailment of some symmetry opera-

tions: that is, formally selecting

subgroups from the group of sym-

metries. We examine the lattice of

subsymmetries of the square (D4).

Figure 2 illustrates all possible

subsymmetries in a hierarchical or-

der: some with four elements; some

with two; and only one, the identity

or asymmetry, with one element.

L··~• •• •L••~D4

Starting from the top of the dia-

gram, Levell, the full symmetry of

the square, D4, forms the superim-

position of the eight distinguish-

able spatial transformations that

comprise this group, including four

quarter-turns and four reflections,

one each about the horizontal and

vertical axes and the leading and

trailing diagonal axes.FIGURE 3. The symmetry group of the square and a typical design, D" formed

by superimposition of representative elements.

Level 2 consists of two reflexive

subsymmetries (D2). One shows

two orthogonal axes (D2vh), and the other shows two diagonal axes at 45° to the orthogonal (D21t).

Both of these subsymmetries exhibit a half-turn through 180°. The D2vh subsymmetry exhibits verti-

cal and horizontal reflections and a half-turn. The D21t subsymmetry exhibits reflections about the

leading and trailing diagonals, as well as a half-turn. The third subsymmetry shows four

quarter-turns, C4, or 90° rotations. The design of C4 forms the superimposition of four spatial trans-

formations: the four quarter-turns with no reflection.

At Level 3, there are five subsymmetries. Four of these subsymmetries include reflective symmetry

DJ: two subsymmetries with a single reflective axis on the orthogonal simple bilateral symmetry (DI v

and Dlh) and two subsymmetries with a single reflective axis on the diagonal (DII and Dlt). The Dlv

subsymmetry exhibits a reflection about the vertical axis only, while the Dlh subsymmetry exhibits a

reflection about the horizontal only. The D II subsymmetry exhibits a reflection about the leading

diagonal only, while the D It subsymmetry exhibits a reflection about the trailing diagonal only. The

fifth subsymmetry at this level, C2, includes only the half-turn rotation. This element has no reflection

axes and no rotation less than the full-turn through 360°. At the bottom level is the unit element, or

the identity of the group, C I' which shows asymmetry, that is, no reflections and no rotations.

As with the examples of regular polygons, such as an equilateral triangle, a pentagon, and others, the

subgroups may be further differentiated according to axes into what we are calling here their

subsymmetries (Park, 2000). A polygon with n edges has, at most, dihedral symmetry of order 2n,where the order of a finite group is the number of elements. The subgroups of the symmetry group of

a regular n-gon are perhaps ordered in the lattice diagram. For instance, D3 is the group of symme-

tries of an equilateral triangle, which has order 6 with its DI, C3, and CI subsymmetries.


[::JD2vh

a

q3r=rql

b c

FIGURE 4. A subgroup of the symmetry of the square formed by the superimposition of the elements ofthe subgroup. (a) Atypical subsymmetry design, 02vl, This subsymmetry exhibits vertical and horizontal reflections and a half-turn. (b) A typicalsubsymmetry design, 021,; it exhibits reflections about the leading and trailing diagonals, as well as a half-turn. (c) A typical

subsymmetry design, C4; it exhibits quarter-turns but no reflections.

Multiplication Table

By multiplying two symmetries ofthe regular polygon, it is possibleto derive another symmetry of thefigure. For example, let us com-bine "q" and "q2r" of the symmetryof the square. The notation [q] [q2r]means mirror reflection [q2r] first,and then rotation [q], reading fromright to left. Since [q][q2r] is asymmetry of the square, the effectmust be one of the 8 symmetrictransformations. In fact, the effectof [q] [q2r] is the same as [q3r]. Ifthose two elements are combinedin a reverse order, then [q2r] [q] isnot the same as [q3r], but [qr].Here, the multiplication order isimportant. The multiple computa-tion of the symmetry of the squareyields a singular result. For in-stance, "qq2rqrqq3rq" is a particu-lar symmetry of the square, so itmust be one of those eight. In factit is the same as "qr." Thus, anycomputation of the symmetries ofthe square concludes with one ofthose eight different transforma-tions.

At this point, it is appropriate todefine a complete structure ofsym-

Diy

a

d

~

q4=i .0

q,!rq, [JDlb

b

DII

e

QDj"

''>; Dq'

C2

c

CI

f

FIGURE 5. A subgroup ofthe symmetry ofthe square formed by the superimpo-sition of the elements of the subgroup. (a) A typical subsymmetry design, °Iv'This subsymmetry exhibits a reflection about the vertical only. (b) A typical

subsymmetry design, Oil,; it exhibits a reflection about the horizontal only. (c)Atypical subsymmetry design, C2; it exhibits a half-turn only. (d) A typical

subsymmetry design, 011; it exhibits a reflection about the leading diagonal only.(e) A typical subsymmetry design, Oft; it exhibits a reflection about the trailingdiagonal only. (f) A typical subsymmetry design, C" formed from the singleelement of the subgroup; it exhibits asymmetry, which has only the identity

motion in its symmetry, without reflections and rotations.


21:1 (Spring, 2004) 29

D[][][2JO·@J[Q][TI"'\ "'\ "'\ : .:"'\ :"'\ :"'\• i·\....J : \.:...J .:...J :.

DDDDDDDDD[JDDDDDDDD[]DDDDDDDD~DDDDDDDDDDDDDDDOD@JDDDDDDDD[Q]DDDODDDDmDDODDODD

FIGURE 6. Multiplication table of the eight elements in the symmetry group of

the square. An element in a column, x, is taken and then multiplied by an

element from a row, y. This gives an element yx which, by closure, is necessarily

one of the eight elements ofthe group.

5'

f-- f--

-'-- -r--

I- f--I

a b

FIGURE 7. Basicparti of the shelter plans: (a) the unit grid, (b) subdivision of

the whole space by the removable closet along the pinwheel type of symmetry.

DESIGN EXAMPLE

metries of a specific group. Arthur

Cayley (1821-1895) introduces the

multiplication table of a group to

determine a finite group, The ele-

ments of the group are displayed in

the top row and in the left column

of the table in the same order; the

entries in the table are the group

products, In general, for a finite

group of order n, there are n2 such

products, which may be conve-

niently listed in an "n x n" multi-

plication table. The table contains

the information on how to multiply

any two symmetries of the figure.

Using the properties of computa-

tion, we construct the multiplica-

tion table of the symmetry group of

order (Figure 6).

Each row and column of the table

is labeled with 8 different symme-

tries. Figure 6 shows all 64 pos-

sible products of ordered pairs of

elements formed by them, as set

out in the table. The product is the

result of multiplying the symmetry

labeling the row by the symmetry

labeling the column. It is expressedby [row] [column]. Again, the com-

putation order is significant. For

example, the 4th row is labeled by

[q3], and the 6th column is labeled

by [q3r], so the product is [q3][q3r]

= [q2r]. In fact, the reverse compu-

tation brings a different effect,

such as [q3r][q3] = [r]. By doing so,

the multiplication tables for any

regular polygons can be written.

There are other depictions of group

structures, such as the Cayley dia-

gram (see Grossman and Magnus,

1964).

In this section, the discussion focuses on the extent to which the formal methodology described above

may apply in the analysis of an architectural design and the synthesis of multiple arrangements of the

design on a city block. The methodology will be applied to the Schindler Shelter developed between

1933 and 1942 by R. M. Schindler. The design was a reaction to the low-cost housing projects for the

Subsistence Homesteads intended to provide urban dwellers with an opportunity to obtain economic

security, as well as comfortable suburban shelter (Park, 1999). Schindler responded to the program

with issues of flexibility of the floor plan, expandability for the changing needs of a growing family,

minimum maintenance, new construction methods, and new materials. A key factor in his proposal


2l:l (Spring, 2004) 30

was to provide a variety of opti-

mum space layouts with the inte-

gration of composition and con-

struction. Schindler developed

various designs based on two dif-

ferent types of construction sys-

tems: the Shell Construction Sys-

tem and the Panel Post Construc-

tion Method. Since schemes of the

Panel Post Construction Method

derive their basic composition

from those of the Shell Construc-

tion, this analysis is confined to the

schemes of the Shell Construction

System. The archival research

verifies that while a series of shel-

ter plans undergo a variety of spatial transformations

for many years, they underlie a unified formative prin-

ciple.

The Spatial Organization of the Project

a b

FIGURE 8. The figure on the left (a) shows a unit group allocated for the

kitchen, bathroom, and laundry. The figure on the right (b) shows the living

room extension.

This discussion focuses primarily on extracting under-

lying principles of spatial organization from the de-

signs. Then, a series of schemata is constructed to de-

scribe its compositional order. Although these sche-

mata may be radically reductive and excessively

simple, they clearly define the compendium of design

logic.

The overall parti of the shelter plans with the Shell

Construction System is set out over a 5 x 5-foot unit

square, although a 4 x 4-foot unit square was used in

laying out the plans of the Panel Post Construction Method. The architect clearly marked the unit on

the drawing (Figure 7a). Along with the unit grid, a pinwheel type of symmetry governed the internal

structure of functional zones in each scheme (Figure 7b). Overlaying the unit grid, the transparent

interplay of a variety of symmetric principles was unique and eminent in Schindler's designs (Park,

1996, 2000, 2001).

FIGURE 9. The garage is a separate unit that could be

added to any side of the house.

The kitchen, bathroom, and laundry were allocated as a unit group to concentrate the plumbing sys-

tems into a single wall (Figure 8a). Using this grouping, supply lines, waste branches, and soil pipes

were simple and short so that the plumbing stack would be saved. Laundry was provided in an open

porch, which afforded an excellent means of open-air drying. The rest of the house was a one-piece

shell. The shell was subdivided into three major rooms. One room was the living room, which ex-

tended a unit module (5-foot) outward from the basic parti of the house for spatial necessity (Figure

8b). The extended module contained the fireplace and the main entry of the shelter. The other two ...

rooms included removable closet partitions for flexible expansion according to the changing needs of

a growing family. The removable closet partitions were set along the pinwheel type of symmetry,

making the central space a hall. The closet was spacious enough and opened alternately into one room

or the other. The clerestory windows above the central hall helped to light and ventilate rooms. The

bathroom was adjacent to the central hall, allowing it to be well-ventilated.

The garage was a separate unit that could be added to any side of the house and that provided spatial

variety from the exterior view (Figure 9). The garage was large enough to serve as a workshop and


21:1 (Spring, 2004) 31

K I.Ltt~!p ~I I I I Gttl I , "u ~ _ ",J==du I

dcba

FIGURE 10. Four different types of spatial configurations ofthe Schindler Shelter: (a) 3-room type (At 852 sq. ft., it includes

a living room, kitchen, and bedroom.); (b) 4-room type (At 1,000 sq. ft., it includes a living room, kitchen, and two bedrooms.);

(c) 4Y,-room type (At 1,040 sq. ft., it includes a living room, kitchen, nook, and two bedrooms); and (d) 5-room type (At 1,194

sq. ft., it includes a living room, kitchen, two bedrooms on the first floor, and a guest room on the second floor.). Key: P = Porch,B = Bedroom, K = Kitchen, L = Living room, G = Garage, H = Hall.

FIGURE 11. Six other variations of the 4-room type: The basic plan is rotated and reflected, and the garage is added based on

the lot location and street line.

storage. Its rooftop provided space for sunbathing. The additional living space and the garage broke

the solid symmetrical juxtaposition of the core parti but produced asymmetrical designs. Breaking the

symmetry exerted another mechanism for the creation of a variety of designs, reinforcing the dynamic

exterior view.

Journal of Architectural and Planning Research21: I (Spring, 2004) 32

Based on archival resources, thereexist four different types of shelterplans, as well as their variations.Their differences are based on thenumber of room types, for ex-ample, 3-, 4-, 4Y2-, and 5-roomtype, as defined by Schindler.

Design Variations and TheirArrangement

G

PA

Since the development of a prefab-ricated housing scheme and itsmass production may result in amonotonous appearance, varia-tions of the prototypical design areimportant. The Schindler Shelterdesigns achieve the quality of thevariations, retaining their unifiedprinciple and remaining un-changed as symmetry transforma-tions take place. The designs alsoincrease a variety of the exteriorappearances with the garage loca-tion. That is the novelty of theSchindler Shelter. Six variations ofa 4-room type scheme were identi-fied by the investigation of the archival drawings. The basic room type was rotated and reflected.Then, a garage was added to a side of the unit. The variations looked different, but a closer observa-tion demonstrated that they were almost identical, based on a unified formative principle.

Street

FIGURE 12. A shelter arrangement of 4-room type variations. Key: E =Entrance, G =Garage, K = Kitchen, L = Living room, P = Porch,

PA = Patio, Y = Yard.

The generation of variations presents further questions on how to arrange the variations in the plan-ning of larger projects. Although the variations could be assembled in a variety of ways, includingend-on units, courts, clustering patterns, or pinwheel format of court patterns, the architect of theSchindler Shelter provided only the street-front pattern of six housing arrangements as an example.The shelters lined both sides of the street, providing independent and easy access to the shelter. Hisexample reflected and rotated only a 4-room type shelter. Garages were added in different locations.No garage was attached to the shelter in the same location as another shelter. Shrubs bordered each lotproperty, providing its own front and back yard. Schindler demonstrated that the change in location ofthe garage and variations of the landscape layout created different street-front designs.

Obviously, when a standard unit and its variations are mixed in different combinations, the possibili-ties of their groupings will be considerably increased. Schindler demonstrates that minor variations ofthe architectural theme in each unit provide differing identities for each dwelling, diminishing itsmonotonous character.

Earlier experiments of symmetric juxtaposition of a housing unit in a large assembly are found invarious housing examples - most notably, the Monolith Homes for Thomas R. Hardy (1919), thePueblo Ribera (1923), and the Harriman project (1924-1925). The Monolith Home stands out as oneofthe earliest housing experiments of this kind. It was developed for F. L. Wright in Racine, Wiscon-sin, while Wright was in Tokyo working on the Imperial Hotel. The spatial composition of the unitplan was set along the strong cross axis. Then, the typical unit plan was assembled in fourquarter-turns, or 90° rotations, in a larger assembly. The same idea was applied to the Pueblo RiberaCourt. There was no strict symmetry involved in the standard unit design, yet the units were grouped

and arranged in four quarter-turns "to ob-

tain a combination (that) achieves archi-

tectural form as a whole" (Schindler,

1949). Subsequently, the idea continued

in the unrealized housing project for J.

Harriman (Gebhard, 1980).


21: I (Spring, 2004) 33

,ttL D"), "cf].. ",i:.:r F.~, '"~ ~L

a b c d

FIGURE 13. Both (a) and (b) are derivatives of the 4-room type. Both (c) and (d) are from the 3-room type. These new designs

underlie the same formative principles ofthe shelter.

rql ql

rq2 rq3 rq4=r

FIGURE 14. Top: The Schindler shelter site with asymmetrical location

of garage marked. Center: Eight sites arranged as a cluster around a

common area. Each site corresponds to one ofthe eight elements in the

symmetry group of the square. Driveways to the garages are shown.

Bottom: Eight clusters arranged around a central open area. Each

cluster corresponds to one ofthe eight elements in the symmetry group

ofthe square. No driveway or garage is directly opposite another across

the street.

The Combinatorial Possibilities ofArranging the Schindler Shelters on aCity Block

A central issue with regard to the analysis

of the project is the synthetic aspect of de-

sign. While a variety of shelter designs

with the unified compositional principle

may exist, the architect never thoroughly

explores all possible layouts. He only pro-

vides some examples of the kind of lay-

outs that he developed. An exhaustive

number of plans could be generated as a

complete map of probable designs. In

generating combinations of possible lay-

outs, symmetry principles as characteris-

tics of form-making are continuously em-

ployed in the design upon which varia-

tions are created.

The application of enumeration prin-

ciples results in huge compositional pos-

sibilities. For example, by manipulating

both the 3- and 4-room types, new designs

are generated by simply rotating and re-

flecting the standard shelter plan and

adding the garage, while still maintaining

formal continuity among them. The de-

signs below are completely new, but ad-

hering to Schindler's principles could


21: I (Spring, 2004) 34

form a possible fam ily of the Schindler

Shelter.

This idea could be extended to regroup the

shelters in a speculative compartmentaliza-

tion of a city site. To illustrate, the shelters

on a city block are arranged in a way Wright

envisions in his Quadruple Building Block

(Wright, 1994). In this example, a hypo-

thetical square lot is represented by the ba-

sic block. On the lot, a simple dot represents

the site of the garage location and driveway

for the orientation of the garage. The dot

corresponds to the symmetry group of the

square. Each block holds eight households

cl ustering around a sem i-pri vate open

space, like Gill's Sierra Madre project of

1910 (McCoy, 1960). Then, eight blocks are

regrouped in a larger assembly that includes

an open community space located in the

middle. Not only can a shelter be arranged

corresponding to one of the eight elements

in the symmetry group of the square, but

variations of different types of the shelters

can also be distinctively combined to generate a huge variety of arrangements, resulting in a variety of

streetscapes. All locations of the shelters with their proper positions are shown in Figure 14.

FIGURE 15. An alternative layout of housing units where each site

corresponds to one of the eight elements in the symmetry group of the

square is shown. Driveways to the garages are shown as well.

Figure 15 is a detailed example of how variations of shelters can be arranged. In this example, 3- and

4-room types of the shelters are arranged in one of the eight clusters. Eight shelters are grouped

within the square lot sharing a central semi-private yard. The open yard provides a well-defined play

area for children, as well as a recreation area for the resident. Each garage attached to, or detached

from, the individual dwelling is connected to the road by a driveway.

In the layout, pergolas, a cantilevered entrance or deck, and a built-in flower box could be attached to

each unit, as Schindler suggested. A row of trees around the entire block at the sidewalk and trees or

shrubs between the units could also be added to provide visual protection, maintain privacy, provide a

relaxing view, and define the border of exclusive space for each lot. The rich landscape could include

shrubs as high as six feet to provide desirable sunlight and privacy.

When illustrated in a three-dimensional perspective, the layout would provide a dynamic look in the

streetscapes as demonstrated in the bird's eye view of the eight-unit cluster (Figure 16). Eye-level

street scenes of the block from each of four corners (Figure 17) provide a glimpse of what the devel-

opment might look like to someone walking by at eye-level (5-foot 6-inch) or driving by in a car

(4-foot). Despite the substantial geometrical similarities of each unit, the streetscape of each side of

the block is distinctive, possessing only a few common configurational properties from the

pedestrian's perspectives. Walking along the streets, pedestrians should enjoy the variety of the street

scenes and a minimization of monotony. The explanation and examples presented in this paper dem-

onstrate how symmetry, with its variations, can be used to create diversity in streetscapes.

CONCLUSION

This paper has explained symmetry and the subsymmetry methodology of the point group as charac-

teristics ofform-making. It serves as a guide to illustrate the specific applications of symmetry group-

ings in the analysis and synthesis of architectural designs. The Schindler Shelter designs are analyzed

Journal of Architectural and Planning Research21:1 (Spring, 2004) 35

FIGURE 16. A perspective rendering showing a variety ofthree-dimensionallooks in the streetscapes.

Pc rspectiv e 1

Perspective 2

Perspective 3

Perspective 4

FIGURE 17. Four eye-level perspective views from each corner ofthe site.


21:1 (Spring, 2004) 36

with regard to the apparent uses of various symmetries in individual designs and their variations,

albeit ambiguous or invisible when seen as a group. The dynamic combinations of symmetric trans-

formations and the external garage lead to unique integral organizations of spatial form.

The garage annexation remarkably augments the performance of symmetric transformations in the

creation of design variety. Compositional ideas defined in the analysis are used in the generation of

new designs where a myriad of possible designs could be produced while preserving a unified forma-

tive principle. In this respect, Schindler's approach excels.

This paper also demonstrates how shelter designs based on symmetric transformations can be clus-

tered on a hypothetical city block. Giving credence to F. L. Wright's quadruple building block, this

study demonstrates that the symmetric transformations of a shelter and its arrangement on a city

block could produce a maximum variety of external facets from any side of the street.

REFERENCES

Alberti LB (1988) On the art of building in ten books. In J Rykwert, et at. (Trs.), Cambridge, MA:

The MIT Press, p. 119.

Budden FJ (1972) Thefascination of groups. London: Cambridge University Press.

Coxeter HSM (Ed.) (1986) Me. Escher: Art and science. Amsterdam: North-Holland.

Emmer M (Ed.) (1993) The visual mind. Cambridge, MA: The MIT Press.

Gebhard D (1980) Schindler. Santa Barbara, CA: Peregrine Smith, Inc.

Grossman I, Magnus W (1964) Groups and their graphs. New York: Random House.

Griinbaum B, Shephard GC (1987) Tilings and patterns. New York: Freeman.

Hargittai I (Ed.) (1986) Symmetry. New York: Pergamon Press.

Hargittai I (Ed.) (1989) Symmetry 2. New York: Pergamon Press.

Lockwood LH, Macmillan RH (1978) Geometric symmetry. Cambridge: Cambridge University

Press.

March L (1979) The modern movement: Symmetry. RIBA 86: 171.

March L, Steadman P (1971) The geometry of environment. London: RIBA Publications Limited.

Martin G (1982) Transformation geometry: An introduction to symmetry. New York: Springer-

Verlag.

McCoy E (1960) Five California architects. New York: Reinhold Publishing Corporation, pp. 83-84.

Park J-H (1996) Schindler, symmetry, and the free public library, 1920. Architectural Research

Quarterly 2(2):72-83.

Park J-H (1999) The architecture of Rudolph Michael Schindler (1887-1953) ~ The formal analysis

of un built work. Unpublished Ph.D. dissertation, University of California, Los Angeles.


Park J-H (2000) Sub symmetry analysis of architectural design: Some examples. Planning and

Design 27:121-136.

Park J-H (2001) Analysis and synthesis in architectural designs: A study in symmetry. Nexus

Network Journal: Architecture and Mathematics 3(1):85-97.

Rosen J (1975) Symmetry discovered: Concepts and applications in nature and science. Cambridge:Cambridge University Press.

Schindler RM (1949) Answer to questionnaire from the School of Architecture, University of South~ern California. Unpublished manuscript,The University of California, Santa Barbara.

Sheine J (2001) R.M Schindler. London: Phaidon Press Limited, pp. 29-33.

Weyl H (1952) Symmetry. Princeton, NJ: Princeton University Press.

Wright FL (1994) Plan by Frank Lloyd Wright. In BB Pfeiffer (Ed.), Frank Lloyd Wright: Collected

writings: 1931-1939. New York: Rizzoli, pp. 139-143.

Yeomans AB (Ed.) (1915) City residential land development studies in planning. Chicago: City Clubof Chicago, pp. 96-102.

Additional information may be obtained by writing directly to Professor Park at the School of Archi-tecture, University of Hawaii at Manoa, 2410 Campus Road, Honolulu, HI 96822, USA; email:j [email protected].

ACKNOWLEDGEMENTS

This paper has been supported in part by a grant from the University Research Council at the University of Hawaii at Manoa.! ammost indebted to Professor Lionel March for his advice and guidance. He has also provided much of the raw material upon whichthis paper is based and some drawings as well. I also wish to thank Professor Michele Emmer for his comments and review of thefinal paper.

AUTOBIOGRAPHICAL SKETCH

Jin-Ho Park, Ph.D., is an assistant professor in the School of Architecture at the University of Hawaii at Manoa. His academicresearch includes Fundamentals of Architectonics: Proportion, Symmetry, and Compartition; The Architecture ofR. M. Schindler(1887-1953); Modern and Contemporary Architectural Design and Theory; Contemporary Los Angeles Architecture; and Designand Computation, including Architecture and Mathematics, Shape Grammars, and Digital Media. He is the author of numerousresearch articles, including "Schindler, Symmetry, and the Free Public Library, 1920" (Architectural Research Quarterly Vol. 2,No.2, (996); "Subsymmetry Analysis of Architectural Designs: Some Examples" (Environment and Planning B: Planning and

Design, Vol. 27, No. 1,2000); and "The Shampay House of 1919: Authorship and Ownership" (Journal of the Society of

Architectural Historians, Vol. 6 I, No.4, 2002).

Manuscript revisions completed 2 February 2003.

Documents

Symmetry and Subsymmetry as Characteristics of Form-Making ...d-lab.kr/prof/2004_01.pdf · elevation even were they all cast in the same mould. A succession ofbuildings of any given