Metagyrate diminished rhombicosidodecahedron

The metagyrate diminished rhombicosidodecahedron, or magydrid, is one of the 92 Johnson solids (J78). It consists of 3×1+6×2 triangles, 3×1+11×2 squares, 3×1+4×2 pentagons, and 1 decagon. It can be constructed by removing one of the pentagonal cupolaic caps of the small rhombicosidodecahedron, and rotating another non-opposite cap by 36º.

Vertex coordinates
A metagyrate diminished 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+$\sqrt{5}$)/4, ±(3+$\sqrt{(5+√5)/2}$)/4, 0)
 * (±1/2, ±1/2, ±(2+$\sqrt{2}$)/2)
 * (±1/2, ±(2+$\sqrt{2}$)/2, ±1/2)
 * (±(2+$\sqrt{5}$)/2, ±1/2, –1/2)
 * (±(1+$\sqrt{11+4√5}$)/4, ±(3+$\sqrt{5}$)/4, ±(1+$\sqrt{3}$)/2)
 * (±(3+$\sqrt{15}$)/4, ±(1+$\sqrt{(65–2√5)/75}$)/2, ±(1+$\sqrt{5}$)/4)
 * (±(1+$\sqrt{(5+√5)/10}$)/2, ±(1+$\sqrt{(5–√5)/10}$)/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)