[clarification needed] The vertex figure of the rectified 5-cell is a uniform triangular prism, formed by three octahedra around the sides, and two tetrahedra on the opposite ends.
In 1997, Tom Braden found another dual pair of examples, by gluing two rectified 5-cells together; since then, infinitely many 2-simple 2-simplicial polytopes have been constructed.
[3][4] It is one of three semiregular 4-polytopes made of two or more cells which are Platonic solids, discovered by Thorold Gosset in his 1900 paper.
The convex hull the rectified 5-cell and its dual (of the same long radius) is a nonuniform polychoron composed of 30 cells: 10 tetrahedra, 20 octahedra (as triangular antiprisms), and 20 vertices.
Thorold Gosset identified this series in 1900 as containing all regular polytope facets, containing all simplexes and orthoplexes (tetrahedrons and octahedrons in the case of the rectified 5-cell).