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About f-Vectors of Inscribed Simplicial Polytopes

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Abstract

We show that for every simplicial polytope an inscribed simplicial polytope exists that has the same dimension, number of vertices, number of edges, and number of 2-faces. This proves that the g-theorem for simplicial polytopes also holds for the class of inscribed simplicial polytopes (up to dimension 7). The proof includes an incremental construction scheme for Delaunay triangulations.

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  1. Inst. Math. and Comp. Sci., FU Berlin, Arnimallee 2, 14195, Berlin, Germany

    Bernd Gonska

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  1. Bernd Gonska
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Correspondence to Bernd Gonska.

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Editor in Charge: Herbert Edelsbrunner and János Pach

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Gonska, B. About f-Vectors of Inscribed Simplicial Polytopes. Discrete Comput Geom 55, 497–521 (2016). https://doi.org/10.1007/s00454-016-9764-8

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