Tri-tridiminished icosahedron

The tri-tridiminished icosahedron, or titdi, is a polyhedron obtained as the dual of the tridiminished icosahedron. It has 3 kites and 3+3 isosceles triangles for faces.

It can be formed from a regular icosahedron by removing 3 sets of 3 vertices, or from a dodecahedron by augmenting 3 non-adjacent faces with tall pyramids.