A unique representation of polyhedral types

Details A unique representation of polyhedral types A unique representation of polyhedral types

2004-01-02

arxiv.org/abs/math/0401005v2

Math. Z. 249 (2005), 513-517

Mathematics

Metric Geometry

4 pages, 2 figures. v2: belated upload of final version (of March 2004)

Scientific paper

10.1007/s00209-004-0713-5

It is known that for each combinatorial type of convex 3-dimensional polyhedra, there is a representative with edges tangent to the unit sphere. This representative is unique up to projective transformations that fix the unit sphere. We show that there is a unique representative (up to congruence) with edges tangent to the unit sphere such that the origin is the barycenter of the points where the edges touch the sphere.

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