Gale transform of a starshaped sphere

Details Gale transform of a starshaped sphere Gale transform of a starshaped sphere

2012-01-30

arxiv.org/abs/1201.6205v1

Mathematics

Combinatorics

21 pages. Affine and convex geometry; combinatorics; Gale transform

Scientific paper

Gale transform is a simple but powerful tool in convex geometry. In particular, the use of Gale transform is the main argument in the classification of polytopes with few vertices. Many books and documents cover the definition of Gale transform and its main properties related to convex polytopes. But it seems that there does not exist document studying the Gale transform of more general objects, such that triangulation of spheres. In this paper, we study the properties of the Gale transform of a large class of such spheres called starshaped spheres.

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