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An indecomposable polytope all of whose facets are decomposable

Published online by Cambridge University Press:  26 February 2010

Zeev Smilansky
Affiliation:
Institute of Mathematics and Computer Science, The Hebrew University of Jerusalem, Givot Ram, 91904 Jerusalem, Israel.
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Extract

A (convex) d-polytope is the convex hull of a finite set of points in Euclidean d–space Ed. The (Minkowski) sum of two polytopes P1 and P2 is defined by

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Type
Research Article
Copyright
Copyright © University College London 1986

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References

1.Grünbaum, B.. Convex Polytopes (Wiley Interscience, 1967).Google Scholar
2.Kallay, M.. Indecomposable Polytopes. Israel J. Math., 41 (1982), 235243.CrossRefGoogle Scholar
3.Kallay, M.. Decomposability of Convex Polytopes. Ph.D. dissertation, Hebrew University of Jerusalem, 1979 (Hebrew, with English summary).Google Scholar
4.Meyer, W. J.. Indecomposable Polytopes. Trans. Amer. Math. Soc., 190 (1974), 7786.CrossRefGoogle Scholar
5.Shephard, G. C.. Decomposable Convex Polyhedra. Mathematika, 10 (1963), 8995.CrossRefGoogle Scholar
6.Smilansky, Z.. Decomposability of Polytopes and Polyhedra, Ph.D. dissertation, Hebrew University of Jerusalem, 1986 (Hebrew, with English summary).CrossRefGoogle Scholar
7.Smilansky, Z.. Decomposability of Polytopes and Polyhedra. To appear in Geometriae Dedicata.Google Scholar