Metabigyrate Rhombicosidodecahedron

The metabigyrate rhombicosidodecahedron is a convex equilateral solid obtained by rotating two of the pentagonal cupolas of a small rhombicosidodecahedron located in the "meta" (in the chemical arene substitution pattern sense) by 1/10 of a turn each. It is Johnson solid .

The unit metabigyrate 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 gyrate rhombicosidodecahedron, parabigyrate rhombicosidodecahedron, small rhombicosidodecahedron, and trigyrate rhombicosidodecahedron (E. Weisstein, Aug. 17, 2023).