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Convex polytopes are the convex hulls of a finite set of points in Euclidean spaces. They have rich combinatorial, arithmetic, and metrical theory, and are related to toric varieties and to linear programming

4 votes
0 answers
82 views

Classification of space-filling (by identical copies) convex polyhedra in R^3

Is the classification of space-filling (by identical copies) convex polyhedra in R^3 is known ? There are only 5 "parallelohedra" - filling by translation. But if relax that property to identical (but …
Alexander Chervov's user avatar
4 votes
1 answer
1k views

Complexity of convex polytope volume calculation ? (Volume of Voronoi cell) (Error probabil...

Assume I have polytope in R^k given by N (k<< N) linear inequalities (A_i x < b_i). I guess complexity of its volume calculate is higher than linear in "N", am I right ? (Is the complexity known ? ) …
Alexander Chervov's user avatar
1 vote
0 answers
58 views

Growth polynomial of the Associahedron graph ? (Is it approximately Gaussian ?)

Consider Associahedron, consider graph build from its vertices and edges. Choose some vertex. Let us count the number of vertices on distances $k$ from the selected vertex. Write a generating polynom …
Alexander Chervov's user avatar