Platonic solid

• platonic solid (US)

From Platonic + solid, in reference to the Greek philosopher Plato, who in his dialogue Timaeus theorised about a correspondence between these solids and the classical physical elements.

Platonic solid (plural Platonic solids)

1. (geometry) Any of five convex polyhedra with congruent regular polygonal faces, which have a high degree of symmetry and have been studied since antiquity.
   • 1961, J. S. Griffith, The Theory of Transition-Metal Ions‎, page 41:

     As the names suggest, the groups and their existence are connected to the five Platonic solids. They are in fact the rotation groups of the Platonic solids.

   • 1993, Aharon Kantorovich, Scientific Discovery: Logic and Tinkering‎, page 160:

     The erroneous number of planets, six, gave him^{[Johannes Kepler]} the clue for his model of five Platonic solids (the five regular convex polyhedra) on which he erected the universe.

   • 2015, Alexander A. Stepanov, Daniel E. Rose, From Mathematics to Generic Programming, page 44,

     In the 13th and final book, he^[Euclid] shows how to construct the five Platonic solids, and proves that they are the only regular polyhedra (bodies whose faces are congruent, regular polygons) that exist.

• (Any of five polyhedra): cube, dodecahedron, icosahedron, octahedron, regular hexahedron (cube), tetrahedron

• Platonic hydrocarbon

• Archimedean solid
• Catalan solid
• Johnson solid
• Kepler solid
• Platonic solid on Wikipedia.Wikipedia
• Regular 4-polytope on Wikipedia.Wikipedia
• List of regular polytopes and compounds on Wikipedia.Wikipedia