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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.
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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

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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.