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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.
Journal of Architectural and Planning Research
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.
Journal of Architectural and Planning Research21: 1 (Spring, 2004) 28
[::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.
Journal of Architectural and Planning Research
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
Journal of Architectural and Planning Research
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
Journal of Architectural and Planning Research
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).
Journal of Architectural and Planning Research
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
Journal of Architectural and Planning Research
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.
Journal of Architectural and Planning Research
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.
Journal of Architectural and Planning Research21: 1 (Spring, 2004) 37
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.