Name
Title | ||
|---|---|---|
Acute triangulations of polyhedra and ℝ<Superscript><Emphasis Type="Italic">N</Emphasis></Superscript> |
Abstract | ||
|---|---|---|
We study the problem of acute triangulations of convex polyhedra and the space ℝ 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 n≥4. Further, we prove that acute triangulations of the space ℝ n do not exist for n≥5. In the opposite direction, in ℝ3, 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 ℝ4 if all dihedral angles are bounded away from π/2. |
Year | DOI | Venue |
|---|---|---|
2012 | 10.1007/s00493-012-2691-2 | Combinatorica |
Keywords | DocType | Volume |
52B05, 52C17, 51M20, 52B10, 52C22 | Journal | 32 |
Issue | ISSN | Citations |
1 | 1439-6912 | 3 |
PageRank | References | Authors |
0.41 | 11 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Eryk Kopczynski | 1 | 64 | 9.68 |
| Igor Pak | 2 | 241 | 43.88 |
| Piotr Przytycki | 3 | 3 | 1.08 |