Pentagonal hexecontahedron
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| Pentagonal hexecontahedron | |
|---|---|
 | |
| Rank | 3 |
| Type | Uniform dual |
| Space | Spherical |
| Notation | |
| Bowers style acronym | Sapedit |
| Coxeter diagram | p5p3p (   ) |
| Elements | |
| Faces | 60 floret pentagons |
| Edges | 30+60+60 |
| Vertices | 12+20+60 |
| Vertex figure | 12 pentagons, 20+60 triangles |
| Measures (edge length 1) | |
| Dihedral angle | ≈ 153.17873° |
| Central density | 1 |
| Related polytopes | |
| Army | Sapedit |
| Regiment | Sapedit |
| Dual | Snub dodecahedron |
| Conjugates | Great pentagonal hexecontahedron, great inverted pentagonal hexecontahedron, great pentagrammic hexecontahedron |
| Abstract & topological properties | |
| Euler characteristic | 2 |
| Surface | Sphere |
| Orientable | Yes |
| Genus | 0 |
| Properties | |
| Symmetry | H3+, order 60 |
| Convex | Yes |
| Nature | Tame |
The pentagonal hexecontahedron, also called the small petaloid ditriacontahedron, is one of the 13 Catalan solids. It has 60 floret pentagons as faces, with 12 order-5 and 20+60 order-3 vertices. It is the dual of the uniform snub dodecahedron.
Each face of this polyhedron is an irregular pentagon with 3 short and 2 long edges. The long edges are around 1.74985 times the length of the shorter ones. Each face has one angle (between two long edges) measuring around 67.45351°, while its other four angles measure around 118.13662°.
External links[edit | edit source]
- Wikipedia Contributors. "Pentagonal hexecontahedron".
- McCooey, David. "Pentagonal Hexecontahedron"