Friday, December 18, 2015

[kppbkxpz] Counting polyhedra

Enumerate polyhedra which are topologically distinct: the graph of adjacencies of faces, edges, and vertices.

Line them up with the natural numbers.  A given polyhedra can encode data, data which can take physical form through 3D printing.

Are "most" polyhedra very weirdly shaped?  Even though we only care about its topological shape, perhaps all instantiations must have a super thin face.  The Szilassi polyhedron looks very spiky.

How many holes does a typical polyhedron of N faces have?  Alternatively, restrict to genus 0.

Restrict to convex only, though this seems hard from just a topological description.

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