Hidden symmetries in the snub dodecahedron (Q1922873)

In a series of papers, F. Hohenberg studied the intersection points of certain pairs of prolonged edges of the Archimedean snub dodecahedron, and he noted that some of these points are the vertices of a regular icosahedron and the 480 remaining ones yield the vertex sets of 8 convex polyhedra having vertex transitivity but no additional symmetry. The author shows that 120 of these 480 intersection points belong to a symmetry plane of the dodecahedron defining the snub dodecahedron. Thus, there are two nearly uniform polyhedra among the 8 obtained ones, therefore the following holds: starting from a chiral polyhedron (without symmetry plane) having regular facets, two polyhedra with full dodecahedral symmetry group but slightly irregular facets are derived. In other words: global symmetry has increased with a loss of local symmetry.