tridiminished icosahedron

It can be obtained by joining a tetrahedron to another Johnson solid, the tridiminished icosahedron.

In geometry, the tridiminished icosahedron is one of the Johnson solids (J).

The tridiminished icosahedron is the vertex figure of the snub 24-cell, a uniform 4-polytope (4-dimensional polytope).

For example, the tridiminished icosahedron starts with a regular icosahedron with 3 vertices removed.

Five Johnson solids have enneahedral duals: the triangular cupola, gyroelongated square pyramid, self-dual elongated square pyramid, triaugmented triangular prism (whose dual is the associahedron), and tridiminished icosahedron.

Other Johnson solids can be formed by cutting off multiple pentagonal pyramids from an icosahedron: the pentagonal antiprism and metabidiminished icosahedron (two pyramids removed), and the tridiminished icosahedron (three pyramids removed).