Disdyakis dodecahedron
| Disdyakis dodecahedron | |
|---|---|
(rotating and 3D model) | |
| Type | Catalan solid |
| Conway notation | mC |
| Coxeter diagram | |
| Face polygon | scalene triangle |
| Faces | 48 |
| Edges | 72 |
| Vertices | 26 = 6 + 8 + 12 |
| Face configuration | V4.6.8 |
| Symmetry group | Oh, B3, [4,3], *432 |
| Dihedral angle | 155° 4' 56" |
| Dual polyhedron | truncated cuboctahedron |
| Properties | convex, face-transitive |
net | |
In geometry, a disdyakis dodecahedron, (also hexoctahedron, hexakis octahedron, octakis cube, octakis hexahedron, kisrhombic dodecahedron) or d48, is a Catalan solid with 48 faces and the dual to the Archimedean truncated cuboctahedron. As such it is face-transitive but with irregular face polygons. It resembles an augmented rhombic dodecahedron. Replacing each face of the rhombic dodecahedron with a flat pyramid results in the Kleetope of the rhombic dodecahedron, which looks almost like the disdyakis dodecahedron, and is topologically equivalent to it. The net of the rhombic dodecahedral pyramid also shares the same topology.