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Regular Skew Polyhedra in Hyperbolic Three-Space

Published online by Cambridge University Press:  20 November 2018

Cyril W. L. Garner
Cyril W. L. Garner*
Affiliation:
Carleton University, Ottawa 1, Ontario
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The study of regular skew polyhedra was initiated in 1926 by Petrie's discovery of two infinite polyhedra in Euclidean three-space E3 which were free of false vertices; the only other regular skew polyhedron in E3 was found by Coxeter (1, pp. 33-34). The simplest of these is denoted {4, 6 | 4} and is derived from the space-filling of cubes by omitting half the faces.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 19 , 1967 , pp. 1179 - 1186
Copyright
Copyright © Canadian Mathematical Society 1967

References

1. Coxeter, H. S. M., Regular skew polyhedra in three and four dimensions, Proc. London Math. Soc. (2), 48 (1937), 33–62.Google Scholar
2. Coxeter, H. S. M., Regular and semi-regular polytopes I, Math. Z.,46 (1940), 380–407.Google Scholar
3. Coxeter, H. S. M., Regular honeycombs in hyperbolic space, Proceedings of the International Congress of Mathematicians (Amsterdam, 1954), Vol. III, pp. 155–169.Google Scholar
4. Coxeter, H. S. M., Symmetrical definitions for the binary polyhedral groups, Proceedings of a Symposium in Pure Mathematics of the American Mathematical Society (New York, 1963), 64–87.Google Scholar
5. Coxeter, H. S. M., Introduction to geometry (New York, 1961).Google Scholar
6. Coxeter, H. S. M., Regular polytopes, 2nd ed. (New York and London, 1963).Google Scholar
7. Klein, F., Vorlesungen über nicht-Euklidischen Geometrie (Berlin, 1928).Google Scholar