Cantellated 5-cell

The convex hull of two cantellated 5-cells in opposite positions is a nonuniform polychoron composed of 100 cells: three kinds of 70 octahedra (10 rectified tetrahedra, 20 triangular antiprisms, 40 triangular antipodiums), 30 tetrahedra (as tetragonal disphenoids), and 60 vertices.

Its vertex figure is a shape topologically equivalent to a cube with a triangular prism attached to one of its square faces.

Vertex figure The cantitruncated 5-cell or great rhombated pentachoron is a uniform 4-polytope.

A double symmetry construction can be made by placing truncated tetrahedra on the truncated octahedra, resulting in a nonuniform polychoron with 10 truncated tetrahedra, 20 hexagonal prisms (as ditrigonal trapezoprisms), two kinds of 80 triangular prisms (20 with D3h symmetry and 60 C2v-symmetric wedges), and 30 tetrahedra (as tetragonal disphenoids).

Vertex figure These polytopes are art of a set of 9 Uniform 4-polytopes constructed from the [3,3,3] Coxeter group.