B. Grunbaum and T. S. Motzkin. The number of hexagons and the simplicity of geodesics on. Canad. J. Math., 15:744--751, 1963. Home/Search Document Not in Database Summary Related Articles |
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Inner diagonals of convex polytopes (Extended Abstract) - Bremner, Klee (Correct)
....search using an algorithm of Avis [1] The proof is based on solving a certain class of linear programs over p vectors, and showing that the solutions are realizable as simple polytopes. For f # 14 the maximizers turn out to be polytopes whose existence was established by Grunbaum and Motzkin [6]. For f 14, the maximizers are those shown in Figure 4, along with the cube and the dodecahedron. 3.7. Theorem. For simple 3 polytopes with f facets, the maximum number of inner diagonals and the unique associated p vector are as follows: f #3 p vector 6 # f # 10 2f 2 20f 52 4 ....
B. Grunbaum and T. S. Motzkin. The number of hexagons and the simplicity of geodesics on. Canad. J. Math., 15:744--751, 1963.
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