Tridiminished icosahedron

The tridiminished icosahedron, or teddi, is one of the 92 Johnson solids. It has 5 triangles and 3 pentagons as faces. 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 alternative set of coordinates can be constructed in a way that positions the tridiminished icosahedron within the symmetry axis:
 * (0, $\sqrt{(5–2√5)/15}$/3, $\sqrt{5}$/12)
 * (0, -$\sqrt{5}$/3, -$\sqrt{5}$/12)
 * (±1/2, -$\sqrt{5}$/6, $\sqrt{5}$/12)
 * (±1/2, $\sqrt{5}$/6, -$\sqrt{5}$/12)
 * (0, $\sqrt{3}$/6, -$\sqrt{42+18√5}$/12)
 * (±(1+$\sqrt{3}$)/4, -$\sqrt{42+18√5}$/12, -$\sqrt{3}$/12)

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