The Platonic solids, Archimedean solids, and the regular prisms and antiprisms are vertex-transitive convex polyhedra with regular polygon faces. Vertex transitivity means that for any two vertices of the polyhedron, there exists a translation, rotation, and/or reflection that leaves the outward appearance of the polyhedron unchanged yet moves one vertex to the other. What happens if the vertex transitivity criterion is removed? As it turns out, there are 92 non-vertex-transitive convex polyhedra with regular polygon faces.

In 1966, Norman Johnson published a paper titled "Convex Polyhedra with Regular Faces" where he described in detail all 92 of these polyhedra. He introduced names for those that weren't named previously, and he mentions that there appear to be no more than 92 of them. These 92 polyhedra are currently known as the Johnson solids. In 1967, Viktor Zalgaller proved that there are no more than 92.

In 2008, Aleksei Timofeenko presented analytically-expressed coordinate values for eight of these polyhedra. It seems most of these values were known only up to numerical approximations previously. For two of these polyhedra, the Bilunabirotunda (J91) and the Triangular Hebesphenorotunda (J92), the values have relatively simple expressions and were probably known prior to Timofeenko's work.

Unlike most polyhedra found in these pages, the Johnson solids have relatively low symmetry orders, and only a few are in canonical form, which makes them unsuitable for automatic generation on a computer. I am grateful to Loïs Mignard-Debise, who spent the time to gather the coordinate values for all 92 polyhedra that are presented here.