Kepler-Poinsot polyhedron

In geometry, a Kepler-Poinsot polyhedron is any of four regular star polyhedra.

One is a regular Kepler-Poinsot polyhedron.

It is one of four compounds constructed from a Platonic solid or Kepler-Poinsot polyhedron and its dual.

A Kepler-Poinsot polyhedron covers its circumscribed sphere more than once, with the centers of faces acting as winding points in the figures which have pentagrammic faces, and the vertices in the others.