The Platonic Solids
by Rüdiger Appel
Platonic solids are perfectly regular solids with the following conditions:
all sides are equal and all angles are the same and all faces are identical.
In each corner of such a solid the same number of surfaces collide.
Only five Platonic solids exist: tetrahedron, hexahedron, octahedron, dodecahedron and icosahedron.
The solids and their regularities were discovered by the Pythagoreans and were called originally Pythagorean solids. The Greek philosopher Plato described the solids in detail later in his book "Timaeus" and assigned the items to the Platonic conception of the world, hence today they are well-known under the name "Platonic Solids.
The five Platonic Solids were thought to represent the five basic elements of the world -- earth, air, fire, water, and the universe.
The tetrahedron is bounded by four equilateral triangles. It has the smallest volume for its surface and represents the property of dryness. It corresponds to fire.
The hexahedron is bounded by six squares. The hexadedron, standing firmly on its base, corresponds to the stable earth.
The octahedron is bounded by eight equilateral triangles. It rotates freely when held by two opposite vertices and corresponds to air.
The dodecahedron is bounded by twelve equilateral pentagons. It corresponds to the universe because the zodiac has twelve signs corresponding to the twelve faces of the dodecahedron.
The icosahedron is bounded by twenty equilateral triangles. It has the largest volume for its surface area and represents the property of wetness. The icosahedron corresponds to water.
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