This Demonstration shows Grünbaum's skeletal polyhedra.
Grünbaum  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].