On infinite 2-orbit polyhedra in classes $$2_0$$ and $$2_2$$

Abstract

We describe all 2-orbit skeletal polyhedra in classes $$2_0$$ 2 0 and $$2_2$$ 2 2 in $$\mathbb {E}^3$$ E 3 . Those in class $$2_2$$ 2 2 are continuous deformations of the three Petrie–Coxeter polyhedra and therefore are arranged in three families. Those in class $$2_0$$ 2 0 are the Petrie duals of the chiral polyhedra in $$\mathbb {E}^3$$ E 3 and are classified in six families.