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Almost Regular Polyhedra

Published online by Cambridge University Press:  03 November 2016

H. G. ApSimon
H. G. ApSimon*
Affiliation:
Decca Research Laboratories
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Extract

In this note I classify certain polyhedra which are of interest in that they have in some sense a higher degree of regularity than any other polyhedra except those which are completely regular. The definition of a regular polyhedron is that it shall possess two particular symmetries; one which cyclically permutes the vertices of any face c, and one which cyclically permutes the faces that meet at a vertex C, C being a vertex of c.

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Type
Research Article
Information
The Mathematical Gazette , Volume 40 , Issue 332 , May 1956, pp. 81 - 85
Copyright
Copyright © Mathematical Association 1956

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References

page 81 note * See, for example, H. S. M. Coxeter, “Regular Skew Polyhedra in Three and Four Dimensions“, Proc. London Math. Soc. (2) 43 (1937), 33-62.

page 82 note * Three Facially-Regular Polyhedra”, Canadian Journ. of Math. 2 (1950) 326-330; “Two Vertex-Regular Polyhedra”, ibid, 3 (1951) 269-271.

page 84 note * For the definitionof this and other terms of this section see Coxeter, “Self-Dual Configurations and Regular Graphs”, Bulletin of American Math. Soc. 56 (1950)