Truncated 120-cells

It is made of 120 truncated dodecahedral and 600 tetrahedral cells.

There are 4800 edges of two types: 3600 shared by three truncated dodecahedra and 1200 are shared by two truncated dodecahedra and one tetrahedron.

Its vertex figure is an equilateral triangular pyramid.

Its vertex figure is a pentagonal pyramid, with one icosahedron on the base, and 5 truncated tetrahedra around the sides.

The truncated tetrahedral cells are joined to each other via their hexagonal faces, and to the icosahedral cells via their triangular faces.