Geometry and Trigonometry

Solid Geometry

What are the Platonic solids?

Platonic solids are also called regular solids, regular figures (a term also used in reference to polygons), regular polyhedra, or “cosmic figures.” These solids are convex polyhedra that have equal faces made up of congruent convex regular polygons. (To compare in terms of a two-dimensional polygon, a regular figure means that both the sides and the angles between them are equal.)


The Greek philosopher Plato first described what are now called platonic solids, polyhedra with equal faces made up of congruent convex regular polygons.

There are considered to only be five of these solids: the cube, dodecahedron icosahedron, octahedron, and tetrahedron. These solids were described by Greek philosopher Plato (c. 428-348 B.C.E.) in his work Timaeus—thus the name Platonic solids. His definitions were certainly more whimsical than today’s, as he believed the major “elements” were made up of atoms shaped like certain polyhedra. He associated the tetrahedron with the “element” fire, the cube with the earth, the icosahedron with water, the octahedron with air, and the dodecahedron with the material that makes up the constellations and heavens. The mathematical proofs of these solids were worked out long ago by Greek mathematician and geometrician Euclid (c. 325-c. 270 B.C.E.) in the last part of his Elements (for more information about Euclid, see elsewhere in this chapter, as well as “Foundations of Mathematics”).


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