Runcinated 120-cells

Its vertex figure is a nonuniform triangular antiprism (equilateral-triangular antipodium): its bases represent a dodecahedron and a tetrahedron, and its flanks represent three triangular prisms and three pentagonal prisms.

The omnitruncated 120-cell or great disprismatohexacosihecatonicosachoron is a convex uniform 4-polytope, composed of 2640 cells: 120 truncated icosidodecahedra, 600 truncated octahedra, 720 decagonal prisms, and 1200 hexagonal prisms.

The vertices and edges form the Cayley graph of the Coxeter group H4.

The first complete physical model of a 3D projection of the omnitruncated 120-cell was built by a team led by Daniel Duddy and David Richter on August 9, 2006 using the Zome system in the London Knowledge Lab for the 2006 Bridges Conference.

[5] The full snub 120-cell or omnisnub 120-cell, defined as an alternation of the omnitruncated 120-cell, can not be made uniform, but it can be given Coxeter diagram , and symmetry [5,3,3]+, and constructed from 1200 octahedrons, 600 icosahedrons, 720 pentagonal antiprisms, 120 snub dodecahedrons, and 7200 tetrahedrons filling the gaps at the deleted vertices.