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The densities of the regular polytopes, Part 2*

Published online by Cambridge University Press:  24 October 2008

H. S. M. Coxeter
H. S. M. Coxeter
Affiliation:
Trinity College
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Extract

Here the notion of density is made more precise, by definition in terms of the fundamental orthoscheme. (The fact that reciprocal polytopes have the same density is a direct consequence of the precise definition.) A new criterion for regular polyhedra is given, superior to Petrie's in that it applies to degenerate, as well as to finite, polyhedra. The cases are examined in which the actual vertex figures of one polytope bound another; and this idea is developed into the process called alternation, which provides an alternative method for calculating density in four dimensions.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 28 , Issue 4 , October 1932 , pp. 509 - 521
Copyright
Copyright © Cambridge Philosophical Society 1932

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References

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