Small ditrigonal icosidodecahedron

It has 32 faces (20 triangles and 12 pentagrams), 60 edges, and 20 vertices.

[1] It has extended Schläfli symbol a{5,3}, as an altered dodecahedron, and Coxeter diagram or .

Its hexagonal vertex figure alternates equilateral triangle and pentagram faces.

It additionally shares its edge arrangement with the great ditrigonal icosidodecahedron (having the triangular faces in common), the ditrigonal dodecadodecahedron (having the pentagrammic faces in common), and the regular compound of five cubes.

As a simple polyhedron, it is also a hexakis truncated icosahedron where the triangles touching the pentagons are made coplanar, making the others concave.