Cantellated 24-cells

There are 2 unique degrees of cantellations of the 24-cell including permutations with truncations.

A half-symmetry construction of the cantellated 24-cell, also called a cantic snub 24-cell, as , has an identical geometry, but its triangular faces are further subdivided.

The difference can be seen in the vertex figures, with edges representing faces in the 4-polytope: The convex hull of two cantellated 24-cells in opposite positions is a nonuniform polychoron composed of 864 cells: 48 cuboctahedra, 144 square antiprisms, 384 octahedra (as triangular antipodiums), 288 tetrahedra (as tetragonal disphenoids), and 576 vertices.

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

The cantitruncated 24-cell or great rhombated icositetrachoron is a uniform 4-polytope derived from the 24-cell.