Metagyrate Diminished Rhombicosidodecahedron

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

The unit metagyrate 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 a nonopposite pentagonal cupola through (Johnson 1966). It can be dissected and reassembled to form the bigyrate diminished rhombicosidodecahedron, diminished rhombicosidodecahedron, or paragyrate diminished rhombicosidodecahedron by rotating the appropriate pentagonal cupolas.