Math in the Middle Institute Partnership


Date of this Version



In partial fulfillment of the requirements for the Master of Arts in Teaching with a Specialization in the Teaching of Middle Level Mathematics in the Department of Mathematics. Jim Lewis, Advisor July 2007


A regular tetrahedron and a regular octahedron are two of the five known Platonic Solids. These five “special” polyhedra look the same from any vertex, their faces are made of the same regular shape, and every edge is identical. The earliest known description of them as a group is found in Plato’s Timaeus, thus the name Platonic Solids. Plato theorized the classical elements were constructed from the regular solids. The tetrahedron was considered representative of fire, the hexahedron or cube represented earth, the octahedron stood for gas or air, the dodecahedron represented vacuum or ether (which is made up of pure electromagnetic energy) , and the icosahedron was water.