Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-15T17:47:18.068Z Has data issue: false hasContentIssue false
  • English
  • Français

Polytopes, Valuations, and the Euler Relation

Published online by Cambridge University Press:  20 November 2018

G. T. Sallee
G. T. Sallee*
Affiliation:
University of California, Davis, California
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

By a d-polytope we shall mean a d-dimensional convex polytope. We shall denote a j-dimensional face (or j-face) of a polytope by Fj. Every d-polytope P has proper j-faces for 0 ≦j ≦d — 1 and we shall also say that P is a d-face of itself. Observe that every face of a polytope is again a polytope. The collection of all convex polytopes shall be denoted by .

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 20 , 1968 , pp. 1412 - 1424
Copyright
Copyright © Canadian Mathematical Society 1968

References

1. Grünbaum, B., Convex polytopes (Wiley, New York, 1967).Google Scholar
2. Hadwiger, H., Vorlesungen ûber Inhalt Oberfiàche und Isoperimetrie (Springer-Verlag, Berlin, 1957).10.1007/978-3-642-94702-5CrossRefGoogle Scholar
3. Hadwiger, H., Uber additive Funktionale k-dimensionaler Eipolyeder, Publ. Math. Debrecen 3 1953), 87–94.Google Scholar
4. Sallee, G. T., A valuation property of Steiner points, Mathematika 13 (1966), 76–82.Google Scholar
5. Sallee, G. T., Incidence graphs of convex polytopes, J. Combinatorial Theory 2 (1967), 466–506.Google Scholar
6. Shephard, G. C., The Steiner point of a convex polytope, Can. J. Math. 18 (1966), 1294–1300.Google Scholar
7. Shephard, G. C., The mean width of a convex polytope, J. London Math. Soc. 1$ (1968), 207–210.10.1112/jlms/s1-43.1.207CrossRefGoogle Scholar
8. Shephard, G. C., Euler-type relations for convex polytopes (to appear).Google Scholar
9. Sommerville, D. M. Y. An introduction to the geometry of n dimensions (Chelsea, New York, 1958).Google Scholar