Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-26T08:38:55.188Z Has data issue: false hasContentIssue false
  • English
  • Français

The Densities of the Regular Polytopes

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

In this paper it is shown how all the regular polytopes (including the Kepler-Poinsot polyhedra and Hess's analogous star polytopes in four dimensions) arise as rational solutions of trigonometrical equations.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 27 , Issue 2 , April 1931 , pp. 201 - 211
Copyright
Copyright © Cambridge Philosophical Society 1931

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

* See Van Oss, S. L., “Die regelmässigen vierdimensionalen Polytopen höherer Art,” Verhandelingen Akad. Wet. Amsterdam, 12 (1915), No. 1.Google Scholar

* Math. Ann. 12 (1877), p. 35.Google Scholar

† In four dimensions, h′ < k 1 and h′ < k 3. In five dimensions, either k 1 < h′ < k 4 or k 1 = h′ = k 4 or k 1 > h′ > k 4.