Disdyakis dodecahedron
Geometric shape with 48 faces / From Wikipedia, the free encyclopedia
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In geometry, a disdyakis dodecahedron, (also hexoctahedron,[1] hexakis octahedron, octakis cube, octakis hexahedron, kisrhombic dodecahedron[2]), 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 creates a polyhedron that looks almost like the disdyakis dodecahedron, and is topologically equivalent to it.
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 |
More formally, the disdyakis dodecahedron is the Kleetope of the rhombic dodecahedron, and the barycentric subdivision of the cube or of the regular octahedron.[3] The net of the rhombic dodecahedral pyramid also shares the same topology.