Acute triangulations of polyhedra and R-N

作者：Kopczynski Eryk^*; Pak Igor; Przytycki Piotr

来源：Combinatorica, 2012, 32(1): 85-110.

DOI：10.1007/s00493-012-2691-2

We study the problem of acute triangulations of convex polyhedra and the space a%26quot;e (n) . Here an acute triangulation is a triangulation into simplices whose dihedral angles are acute. We prove that acute triangulations of the n-cube do not exist for na parts per thousand yen4. Further, we prove that acute triangulations of the space a%26quot;e (n) do not exist for na parts per thousand yen5. In the opposite direction, in a%26quot;e(3), we present a construction of an acute triangulation of the cube, the regular octahedron and a non-trivial acute triangulation of the regular tetrahedron. We also prove nonexistence of an acute triangulation of a%26quot;e(4) if all dihedral angles are bounded away from pi/2.

• 出版日期2012-1