Name
Abstract | ||
|---|---|---|
In this paper we consider geodesic triangulations of the surface of the regular dodecahedron. We are especially interested in triangulations with angles not larger than @p/2, with as few triangles as possible. The obvious triangulation obtained by taking the centres of all faces consists of 20 acute triangles. We show that there exists a geodesic triangulation with only 10 non-obtuse triangles, and that this is best possible. We also prove the existence of a geodesic triangulation with 14 acute triangles, and the non-existence of such triangulations with less than 12 triangles. |
Year | DOI | Venue |
|---|---|---|
2007 | 10.1016/j.ejc.2006.04.008 | Eur. J. Comb. |
Keywords | Field | DocType |
obvious triangulation,acute triangulations,geodesic triangulations,regular dodecahedron,acute triangle,regular dodecahedral surface,geodesic triangulation,non-obtuse triangle | Discrete mathematics,Combinatorics,Icosahedron,CPCTC,Triangulation (social science),Dodecahedron,Mathematics,Geodesic,Delaunay triangulation | Journal |
Volume | Issue | ISSN |
28 | 4 | 0195-6698 |
Citations | PageRank | References |
7 | 0.69 | 7 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Jin-ichi Itoh | 1 | 47 | 10.17 |
| Tudor Zamfirescu | 2 | 77 | 16.85 |