Pentagonal hexecontahedron
In geometry, a pentagonal hexecontahedron is a Catalan solid, dual of the snub dodecahedron. It has two distinct forms, which are mirror images (or "enantiomorphs") of each other. It has 92 vertices that span 60 pentagonal faces. It is the Catalan solid with the most vertices. Among the Catalan and Archimedean solids, it has the second largest number of vertices, after the truncated icosidodecahedron, which has 120 vertices.
| Pentagonal hexecontahedron | |
|---|---|
(Click here for rotating model) | |
| Type | Catalan solid |
| Coxeter diagram | |
| Conway notation | gD |
| Face type | V3.3.3.3.5 irregular pentagon |
| Faces | 60 |
| Edges | 150 |
| Vertices | 92 |
| Vertices by type | 12 {5} 20+60 {3} |
| Symmetry group | I, 1/2H3, [5,3]+, (532) |
| Rotation group | I, [5,3]+, (532) |
| Dihedral angle | 153°10′43″ |
| Properties | convex, face-transitive chiral |
Snub dodecahedron (dual polyhedron) |
Net |
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