The Demiurge, or divine craftsman in Plato's Timeaus is also a mathematician, and has constructed the cosmos according to geometrical principles.
Influenced by the Pythagorean program of reducing everything to first principles, Plato takes the four elements of which all matter is composed- earth, water, air and fire - and reduces them to triangles. These fundamental triangles, if suitably combined, can be made into the only five geometrical solids known to exist. Plato then assigned each of these geometric solids to a different element: fire was associated with the tetrahedron (four equilateral triangles), the smallest, sharpest and most mobile of the regular solids; air with the octahedron (eight equilateral triangles); water with the icosahedron (twenty equilateral triangles); and earth with the cube (six squares), the most stable of the regular solids. The fifth solid, the dodecahedron (twelve pentagons), is closest in form to the sphere, and is therefore identified with the cosmos as a whole.
Plato's cosmic scheme, based on geometric solids, also accounts for change, diversity and transmutation of the physical universe, because the elements (all based on fundamental triangles) can mix in various proportions to produce variety in the material world. (Only earth is excluded from this transmutability because it is composed of squares which when divided diagonally do not yield two equilateral triangles).*
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