Three Theorems, with Computer-Aided Proofs, on Three-Dimensional Faces and Quotients of Polytopes
Copyright policy )Three Theorems, with Computer-Aided Proofs, on Three-Dimensional Faces and Quotients of Polytopes
The authors prove three theorems: 1. There is a finite list of three-dimensional polytopes such that every rational 9-polytope contains a three-dimensional face in the list. 2. Every nine-dimensional polytope has the three-dimensional simplex as a quotient. 3. Every 5-polytope contains a three-dimensional quotient with at most eight vertices. The proof relies on the computer program FLAGTOOL which computes all (known) relations between the flag numbers of general \(d\)-polytopes for small dimensions.
- Hebrew University of Jerusalem Israel
- University of Passau Germany
rational polytope, flag numbers, Eulerian lattice, Three-dimensional polytopes, quotient of a polytope, \(n\)-dimensional polytopes
rational polytope, flag numbers, Eulerian lattice, Three-dimensional polytopes, quotient of a polytope, \(n\)-dimensional polytopes
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