Two-dimensionally infinite polyhedra with vertices related by symmetry operations.
It is shown that an infinitely extended polyhedron of one sheet composed of plane polygons of finite size, and in which all the vertices are related to one another by symmetry operations, can always be constructed by folding a stiff, unstretchable sheet (such as a piece of paper). It is also shown that only 11 such polyhedra have faces that are regular polygons; these polygons are equilateral triangles and squares. The 4 of these 11 polyhedra that are not known to have been published previously are presented here.
Harker
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Medical Foundation of Buffalo, Inc., Buffalo, NY 14203, USA.