Name
Abstract | ||
|---|---|---|
We study the problem of acute triangulations of convex polyhedra and the space ℜn. 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 ℜn do not exist for n ≥ 5. In the opposite direction, in ℜ3 we construct nontrivial acute triangulations of all Platonic solids. We also prove nonexistence of an acute triangulation of ℜ4 if all dihedral angles are bounded away from ϒ/2. |
Year | DOI | Venue |
|---|---|---|
2010 | 10.1145/1810959.1811010 | Symposium on Computational Geometry 2013 |
Keywords | Field | DocType |
acute triangulation,opposite direction,acute triangulations,nontrivial acute triangulations,platonic solid,convex polyhedron,dihedral angle,euclidean space,polyhedra | Discrete mathematics,Combinatorics,Platonic solid,Polyhedron,Euclidean space,Regular polygon,Triangulation (social science),Dihedral angle,Mathematics,Bounded function | Conference |
Citations | PageRank | References |
0 | 0.34 | 13 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Eryk Kopczynski | 1 | 64 | 9.68 |
| Igor Pak | 2 | 241 | 43.88 |
| Piotr Przytycki | 3 | 3 | 1.08 |