The plastic beauty of polyhedra, seen in isolation or in combinations, cannot leave a sensitive observer cold. The architect, in particular, is attracted by the unexpected spaces found inside polyhedra as well as by the rhythmical geometry of their polygonal faces. This fascination can be understood by the wilfulness of most architectural forms and compositions when compared with the inevitability of pure geometry.

The temptation to see in infinite structures or close-packing systems practical means for flexible, modular building systems has not produced the anticipated crop of masterpieces. Yet, the potential for architecture of the extraordinary forms, patterns and relationships provided by polyhedra does exist. But this potential may be more appropriate to the design of unique buildings than to mass production.

Eleven patterns involving ten polyhedra were subjected to careful study for several years in the author's design studios at Syracuse University and at the Massachusetts Institute of Technology. They all revealed substantial architectural merits. Some aspects of these patterns are discussed here.

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