Paragyrate Diminished Rhombicosidodecahedron

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

The unit paragyrate diminished rhombicosidodecahedron has volume

(1)

and Dehn invariant

			(2)
			(3)

where the first expression uses the basis of Conway et al. (1999). It is obtained from the small rhombicosidodecahedron by removing one pentagonal cupola and rotating the opposite pentagonal cupola through (Johnson 1966). It can be dissected and reassembled to form the bigyrate diminished rhombicosidodecahedron, diminished rhombicosidodecahedron, or metagyrate diminished rhombicosidodecahedron by rotating the appropriate pentagonal cupolas.