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Platonic Solids

polyhedra whose faces are all congruent regular pologonos are called "regular polyhedra" or "Platonic solids." There are only five:

• regular tetrahedron (4 vertices, 6 edges, 4 equilateral triangles as faces)
  



• regular hexahedron or cube (8 vertices, 12 edges, 6 squares as faces)
  



• regular octahedron (6 vertices, 12 edges, 8 equilateral triangles as faces)
  



• regular dodecahedron (20 vertices, 30 edges, 12 pentagons as faces)
  



• regular icosahedron (12 vertices, 30 edges, 20 equilateral triangles as faces)
  

This is known since the days of classical Greece, and its "rarity" explains the fascination that these bodies have exercised throughout history.

The ancient Greeks associated each of the regular polyhedra the elements composing the universe. Plato in his Timaeus, associated with each of the four elements that the Greeks were the universe, fire, air, water and land to a polyhedron: tetrahedron fire, air the octahedron, icosahedron and ground water at the hexahedron or cube. Finally
associated the last regular polyhedron, the dodecahedron, the Universe. For this reason, these polyhedra are called Platonic solids. You can see a representation of polyhedra by Kepler, which is represented this association.

prefixes Tetra, Hexa, Octa, and Icosa Dodeca that give name to the five regular polyhedra indicate the number of polygons (faces) that form the body