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