Faceted hexacosichoron

The faceted hexacosichoron, or fix, also commonly called the icosahedral 120-cell, is one of the 10 Schläfli–Hess polychora. It has 120 icosahedra as cells, joining 5 to an edge and 12 to a vertex in the form of a great dodecahedron.

As the name suggests, it is a faceting of the hexacosichoron, sharing its vertices, edges, and faces. The icosahedral cells are the same as the vertex figures of the hexacosichoron.

Vertex coordinates
Its vertices are the same as those of its regiment colonel, the hexacosichoron.