Gyrate bidiminished rhombicosidodecahedron

The gyrate bidiminished rhombicosidodecahedron, or gybadrid, is one of the 92 Johnson solids (J82). It consists of 4×1+3×2 triangles, 4×1+8×2 squares, 4×1+3×2 pentagons, and 2 decagons. It can be constructed by removing two non-opposite pentagonal cupolaic caps of the small rhombicosidodecahedron, and rotating a third cap by 36º.

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