A Periodic Table of Polyhedra

Not a selection — a census. These 127 solids are the union of five classifications that are each provably complete: the five Platonic solids, the thirteen Archimedean, their thirteen Catalan duals, the ninety-two Johnson solids, and the four Kepler–Poinsot stars. Nothing has been left out except the prisms and antiprisms, which run to infinity and cannot fit in a column.

Columns are the number of kinds of face a solid has — how many classes its symmetry group divides its faces into. That falls from left to right, so the table runs from the lopsided to the perfectly uniform, ending in the nine solids that are transitive on vertices, edges and faces at once. Those are the noble gases: nothing about them can be made more regular.