Great rhombihexacron

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] 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.

Each bow-tie has two angles of

arccos ⁡ (

arccos ⁡ ( −

The diagonals of each bow-tie intersect at an angle of

The dihedral angle equals

The ratio between the lengths of the long edges and the short ones equals