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An indecomposable polytope all of whose facets are decomposable

  • Zeev Smilansky (a1)


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