Hostname: page-component-6b989bf9dc-wj8jn Total loading time: 0 Render date: 2024-04-15T00:58:41.775Z Has data issue: false hasContentIssue false

Uniform compounds of uniform polyhedra

Published online by Cambridge University Press:  24 October 2008

J. Skilling
Affiliation:
Department of Applied Mathematics and Theoretical Physics, Silver Street, Cambridge

Abstract

The work of Coxeter, Longuet-Higgins and Miller (1953) and of Skilling (1975) is extended to give a complete list of uniform compounds of uniform polyhedra. Symmetry relationships between polyhedra and their compounds are discussed.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1976

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

(1)Coxeter, H. S. M., Longuet-Higgins, M. S. and Miller, J. C. P.Uniform polyhedra. Philos. Trans. Roy. Soc. L. Ser. A 246 (1953), 401450.Google Scholar
(2)Coxeter, H. S. M. and Moser, W. O. J.Generators and relation for discrete groups, 2nd edn. (Berlin: Springer-Verlag, 1965), 135.Google Scholar
(3)Norman, A. C. and Smith, A.Computer drawings of compounds of star polyhedra. Math. Gazette 57 (1973), 303306.CrossRefGoogle Scholar
(4)Skilling, J.The complete set of uniform polyhedra. Philos. Trans. Roy. Soc. Lond. Ser. A 278 (1975), 111135.Google Scholar
(5)Smith, A.Uniform compounds and the group 4. Proc. Cambridge Philos. Soc. 75 (1974), 115117.CrossRefGoogle Scholar
(6)Sopov, S. P.Proof of completeness of the list of uniform polyhedra. Ukrain. Geometr. Sb. 8 (1970), 139156.Google Scholar