This Demonstration shows Grünbaum's skeletal polyhedra.

Grünbaum [2] discovered nine regular skeletal polyhedra whose faces are regular skew polygons. Five of them are obtained from the Platonic solids and four from the Kepler–Poinsot polyhedra. To find a skew face in one of them, trace a path along its edges such that each pair of adjacent edges are sides of a face of the polyhedron but no three consecutive edges are sides of a single face. The polygon constructed is called a Petrie polygon [1, pp. 284–285].