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An Enumeration of the Five Parallelohedra

Published online by Cambridge University Press:  20 November 2018

William Moser
William Moser*
Affiliation:
University of Manitoba
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A parallelohedron is a convex polyhedron, in real affine three-dimensional space, which can be repeated by translation to fill the whole space without interstices. It has centrally symmetrical faces [4, p. 120] and hence is centrally symmetrical.

Let Fi denote the number of faces each having exactly i edges, Vi denote the number of vertices each incident with exactly i edges, E denote the number of edges, n denote the number of sets of parallel edges, F denote the total number of faces, V denote the total number of vertices.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 4 , Issue 1 , January 1961 , pp. 45 - 47
Copyright
Copyright © Canadian Mathematical Society 1961

References

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