The Johnson Solids are the convex polyhedra having regular faces and equal edge lengths (with the exception of the completely regular Platonic solids, the “semiregular” Archimedean solids, and the two infinite families of prisms and antiprisms). There are 28 simple (i.e., cannot be dissected into two other regular-faced polyhedra by a plane) regular-faced polyhedra in addition to the prisms and antiprisms (Zalgaller 1969), and Johnson (1966) proposed and Zalgaller (1969) proved that there exist exactly 92 Johnson solids in all. They are implemented in Mathematica as Polyhedron Data.
