Diminished Rhombicosidodecahedron

The diminished rhombicosidodecahedron is a convex equilateral solid that is Johnson solid .

This solid is the diminished polyhedron obtained by diminishing a small rhombicosidodecahedron by one of its pentagonal cupolas.

The unit diminished rhombicosidodecahedron has volume

(1)

and Dehn invariant

			(2)
			(3)

where the first expression uses the basis of Conway et al. (1999). It can be dissected into the bigyrate diminished rhombicosidodecahedron, metagyrate diminished rhombicosidodecahedron, and paragyrate diminished rhombicosidodecahedron, all of which differ only by rotation of one or more pentagonal cupolas.