Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-29T19:05:36.983Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Brückner, 1, Vielecke und Vielflache (Leipzig, 1900).Google Scholar
Coxeter, 1, Phil. Trans. Royal Soc. A, 229, pp. 329–425 (1930).Google Scholar
Coxeter, 2, Proc. London Math. Soc., 34, pp. 126–189 (1932).CrossRefGoogle Scholar
Schläfli, 1, Journal de Math., 20, pp. 359–394 (1855).Google Scholar
Schläfli, 2, Neue Denkschr. d. allg. schweiz. Gesells. f. d. gesammten Naturwiss., 38 (1901).Google Scholar
Todd, 1, Proc. Camb. Phil. Soc., 27, pp. 212–231 (1931).CrossRefGoogle Scholar