Truncated 5-cell

The diagonal f-vector numbers are derived through the Wythoff construction, dividing the full group order of a subgroup order by removing one mirror at a time.

These coordinates come from positive orthant facets of the truncated pentacross and bitruncated penteract respectively.

The convex hull of the truncated 5-cell and its dual (assuming that they are congruent) is a nonuniform polychoron composed of 60 cells: 10 tetrahedra, 20 octahedra (as triangular antiprisms), 30 tetrahedra (as tetragonal disphenoids), and 40 vertices.

Topologically, under its highest symmetry, [[3,3,3]], there is only one geometrical form, containing 10 uniform truncated tetrahedra.

-dimensional analog is the polytope whose Coxeter–Dynkin diagram is linear with rings on the middle one or two nodes.

The diagonal f-vector numbers are derived through the Wythoff construction, dividing the full group order of a subgroup order by removing one mirror at a time.

The dual regular skew polyhedron, {4,6|3}, is similarly related to the square faces of the runcinated 5-cell.

Being the dual of a uniform polychoron, it is cell-transitive, consisting of 30 congruent tetragonal disphenoids.

These polytope are from a set of 9 uniform 4-polytope constructed from the [3,3,3] Coxeter group.