A solid angle theory for real polytopes

Details A solid angle theory for real polytopes A solid angle theory for real polytopes

2007-07-31

arxiv.org/abs/0708.0042v1

Mathematics

Combinatorics

18 pages

Scientific paper

We extend many theorems from the context of solid angle sums over rational polytopes to the context of solid angle sums over real polytopes. Moreover, we consider any real dilation parameter, as opposed to the traditional integer dilation parameters. One of the main results is an extension of Macdonald's solid angle quasipolynomial for rational polytopes to a real analytic function of the dilation parameter, for any real convex polytope.

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