Great rhombihexacron

Great rhombihexacron
Type	Star polyhedron
Face
Elements	F = 24, E = 48 V = 18 (χ = −6)
Symmetry group	Oh, [4,3], *432
Index references	DU21
dual polyhedron	Great rhombihexahedron

In geometry, the great rhombihexacron 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]

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.

Notes

References

• Wenninger, Magnus (1983), Dual Models, Cambridge University Press, ISBN 978-0-521-54325-5, MR 0730208
• uniform polyhedra and duals