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Two-dimensionally infinite polyhedra with vertices related by symmetry operations.
MedLine Citation:
PMID:  11607148     Owner:  NLM     Status:  PubMed-not-MEDLINE    
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.
D Harker
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Publication Detail:
Type:  Journal Article    
Journal Detail:
Title:  Proceedings of the National Academy of Sciences of the United States of America     Volume:  88     ISSN:  0027-8424     ISO Abbreviation:  Proc. Natl. Acad. Sci. U.S.A.     Publication Date:  1991 Jan 
Date Detail:
Created Date:  2001-10-18     Completed Date:  2001-12-28     Revised Date:  2008-11-20    
Medline Journal Info:
Nlm Unique ID:  7505876     Medline TA:  Proc Natl Acad Sci U S A     Country:  United States    
Other Details:
Languages:  eng     Pagination:  585-7     Citation Subset:  -    
Medical Foundation of Buffalo, Inc., Buffalo, NY 14203, USA.
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