An Enumeration of the Five Parallelohedra
Canadian mathematical bulletin, Tome 4 (1961) no. 1, pp. 45-47
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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.
Moser, William. An Enumeration of the Five Parallelohedra. Canadian mathematical bulletin, Tome 4 (1961) no. 1, pp. 45-47. doi: 10.4153/CMB-1961-007-7
@article{10_4153_CMB_1961_007_7,
author = {Moser, William},
title = {An {Enumeration} of the {Five} {Parallelohedra}},
journal = {Canadian mathematical bulletin},
pages = {45--47},
year = {1961},
volume = {4},
number = {1},
doi = {10.4153/CMB-1961-007-7},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1961-007-7/}
}
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