![cover image](https://wikiwandv2-19431.kxcdn.com/_next/image?url=https://upload.wikimedia.org/wikipedia/commons/thumb/a/ac/DU21_great_rhombihexacron.png/640px-DU21_great_rhombihexacron.png&w=640&q=50)
Great rhombihexacron
Polyhedron with 24 faces / From Wikipedia, the free encyclopedia
In geometry, the great rhombihexacron (or great dipteral disdodecahedron) is a nonconvex isohedral polyhedron. It is the dual of the uniform great rhombihexahedron (U21).[1] It has 24 identical bow-tie-shaped faces, 18 vertices, and 48 edges.[2]
Great rhombihexacron | |
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Type | Star polyhedron |
Face | ![]() |
Elements | F = 24, E = 48 V = 18 (Ļ = ā6) |
Symmetry group | Oh, [4,3], *432 |
Index references | DU21 |
dual polyhedron | Great rhombihexahedron |
It has 12 outer vertices which have the same vertex arrangement as the cuboctahedron, and 6 inner vertices with the vertex arrangement of an octahedron.
As a surface geometry, it can be seen as visually similar to a Catalan solid, the disdyakis dodecahedron, with much taller rhombus-based pyramids joined to each face of a rhombic dodecahedron.