| Extremal Properties for Dissections of Convex Polytopes (2007) | |||||||||||||||
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| . A dissection of a convex d-polytope is a partition of the polytope into d-simplices whose vertices are among the vertices of the polytope. Triangulations are dissections that have the additional property that the set of all its simplices forms a simplicial complex. The size of a dissection is the number of d-simplices it contains. This paper compares triangulations of maximal size with dissections of maximal size. We also exhibit lower and upper bounds for the size of dissections of a 3-polytope and analyze extremal size triangulations for specific non-simplicial polytopes: prisms, antiprisms, Archimedean solids, and combinatorial d-cubes. Key words. dissection; triangulation; mismatched region; lattice polytope; combinatorial d- cube; prism; antiprism; Archimedean solid AMS subject classifications. 52B45, 52B05, 52B70, 52B55. 1. Introduction. Let A be a point configuration in R d with its convex hull conv(A) having dimension d. A set of d-simplices with vertices in A is a disse... | |||||||||||||||
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