Pentagonal pyramid

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 2 has the following vertices:

(–(1+$\sqrt{5}$)/4, 0, ±1/2)
 * (0, 1/2, (1+$\sqrt{5}$)/4)
 * (0, ±1/2, –ª1+$\sqrt{5}$)/4)
 * (1/2, (1+$\sqrt{(5+√5)/8}$)/4, 0)
 * (±1/2, –(1+$\sqrt{5}$)/4, 0)
 * ((1+$\sqrt{5}$)/4, 0, 1/2)

These are the vertices of an icosahedron with 3 poits removed.