Diminished rhombicosidodecahedron

The diminished rhombicosidodecahedron, or dirid, is one of the 92 Johnson solids (J76). It consists of 5+5+5 triangles, 5+5+5+10 squares, 1+5+5 pentagons, and 1 decagon. It can be constructed by removing one of the pentagonal cupolaic caps of the small rhombicosidodecahedron.

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