Acute triangulations of polyhedra and R^n - Mathematics > Metric GeometryReportar como inadecuado




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Abstract: We study the problem of acute triangulations of convex polyhedra and thespace R^n. Here an acute triangulation is a triangulation into simplices whosedihedral angles are acute. We prove that acute triangulations of the n-cube donot exist for n>=4. Further, we prove that acute triangulations of the spaceR^n do not exist for n>= 5. In the opposite direction, in R^3, we present aconstruction of an acute triangulation of the cube, the regular octahedron anda non-trivial acute triangulation of the regular tetrahedron. We also provenonexistence of an acute triangulation of R^4 if all dihedral angles arebounded away from pi-2.



Autor: Eryk Kopczyński, Igor Pak, Piotr Przytycki

Fuente: https://arxiv.org/







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