Gyrate Rhombicosidodecahedron

The gyrate rhombicosidodecahedron is a convex equilateral solid obtained by rotating one of the pentagonal cupolas of a small rhombicosidodecahedron by 1/10 of a turn. It is Johnson solid .

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