Metabigyrate rhombicosidodecahedron

The metabigyrate rhombicosidodecahedron, or mabgyrid, is one of the 92 Johnson solids (J74). It consists of 2+2+2+2+4+4+4 triangles, 1+1+2+2+4+4+4+4+4+4 squares, and 2+2+2+2+4 pentagons. It can be constructed by rotating two non-opposite pentagonal cupolaic caps of the small rhombicosidodecahedron by 36º.

Vertex coordinates
A metabigyrate rhombicosidodecahedron of edge length 1 has vertices given by:
 * (0, ±(5+$\sqrt{2}$)/4, ±(3+$\sqrt{5}$)/4)
 * (±(3+$\sqrt{2}$)/4, 0, –(5+$\sqrt{2}$)/4)
 * (±(5+$\sqrt{2}$)/4, ±(3+$\sqrt{5}$)/4, 0)
 * (±1/2, ±1/2, ±(2+$\sqrt{11+4√5}$)/2)
 * (±1/2, ±(2+$\sqrt{5}$)/2, ±1/2)
 * (±(2+$\sqrt{3}$)/2, ±1/2, –1/2)
 * (±(1+$\sqrt{15}$)/4, ±(3+$\sqrt{(65–2√5)/75}$)/4, ±(1+$\sqrt{5}$)/2)
 * (±(3+$\sqrt{(5+√5)/10}$)/4, ±(1+$\sqrt{5}$)/2, ±(1+$\sqrt{5}$)/4)
 * (±(1+$\sqrt{5}$)/2, ±(1+$\sqrt{5}$)/4, –(3+$\sqrt{5}$)/4)
 * (±(5+4$\sqrt{5}$)/10, ±1/2, (10+3$\sqrt{5}$)/20)
 * (±(5+2$\sqrt{5}$)/5, ±(1+$\sqrt{5}$)/4, (15+$\sqrt{5}$)/20)
 * (±(15+13$\sqrt{5}$)/20, 0, (5+$\sqrt{5}$)/20)