Tridiminished icosahedron

The tridiminished icosahedron, or teddi, is one of the 92 Johnson solids (J63). It consists of 1+1+3 triangles and 3 pentagons. It can be constructed by removing 3 mutually non-adjacent vertices from a regular icosahedron.

Vertex coordinates
A tridiminished icosahedron of edge length 1 has the following vertices:
 * (0, 1/2, (1+$\sqrt{5}$)/4),
 * (0, ±1/2, –(1+$\sqrt{5}$)/4),
 * (1/2, (1+$\sqrt{5}$)/4, 0),
 * (±1/2, –(1+$\sqrt{(5+√5)/8}$)/4, 0),
 * ((1+$\sqrt{5}$)/4, 0, 1/2),
 * (–(1+$\sqrt{5}$)/4, 0, ±1/2).

These are the vertices of an icosahedron, but with three missing.

An alternate set of coordinates can be given in a way that positions the tridiminished icosahedron within the symmetry axis:
 * (±1/2, –$\sqrt{(5–2√5)/15}$/6, ($\sqrt{5}$+$\sqrt{5}$)/6),
 * (0, $\sqrt{5}$/3, ($\sqrt{5}$+$\sqrt{5}$)/6),
 * (±(1+$\sqrt{5}$)/4, –($\sqrt{5}$+$\sqrt{3}$)/12, 0),
 * (0, ($\sqrt{3}$+$\sqrt{15}$)/6, 0),
 * (±1/2, $\sqrt{3}$/6, –$\sqrt{3}$/3),
 * (0, –$\sqrt{15}$/3, –$\sqrt{5}$/3).

Related polyhedra
A tetrahedron can be attached to the tridiminished icosahedron at the triangular face surrounded by pentagons to form the augmented tridiminished icosahedron.