Pentagonal icositetrahedron
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| Pentagonal icositetrahedron | |
|---|---|
 | |
| Rank | 3 |
| Type | Uniform dual |
| Space | Spherical |
| Notation | |
| Bowers style acronym | Pedid |
| Coxeter diagram | p4p3p (   ) |
| Elements | |
| Faces | 24 floret pentagons |
| Edges | 12+24+24 |
| Vertices | 6+8+24 |
| Vertex figure | 6 squares, 8+24 triangles |
| Measures (edge length 1) | |
| Dihedral angle | ≈ 136.30923° |
| Central density | 1 |
| Number of external pieces | 24 |
| Level of complexity | 10 |
| Related polytopes | |
| Army | Pedid |
| Regiment | Pedid |
| Dual | Snub cube |
| Conjugate | Pentagonal icositetrahedron |
| Abstract & topological properties | |
| Flag count | 240 |
| Euler characteristic | 2 |
| Surface | Sphere |
| Orientable | Yes |
| Genus | 0 |
| Properties | |
| Symmetry | B3+, order 24 |
| Convex | Yes |
| Nature | Tame |
The pentagonal icositetrahedron, also called the petaloid disdodecahedron or pedid, is one of the 13 Catalan solids. It has 24 floret pentagons as faces, with 6 order-4 and 8+24 order-3 vertices. It is the dual of the uniform snub cube.
Each face of this polyhedron is an irregular pentagon with 3 short and 2 long edges. The long edges are around 1.41964 times the length of the shorter ones. Each face has one angle (between two long edges) measuring around 80.75170°, while its other four angles measure around 114.81207°.
External links[edit | edit source]
- Wikipedia Contributors. "Pentagonal icositetrahedron".
- McCooey, David. "Pentagonal Icositetrahedron"