# Platonic Solids.

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Platonic Solids

PLATO "Let no one destitute of geometry enter my doors."

Plato was a Classical Greek philosopher ,mathematician, writer of philosophical dialogues, and founder of the Academy in Athens, the first institution of higher learning in the Western world . Along with his mentor, Socrates, and his student, Aristotle, Plato helped to lay the foundations of Western philosophy and science. Plato was originally a student of Socrates, and was as much influenced by his thinking as by his apparently unjust execution.

Platonic Solids The so-called Platonic Solids are regular Polyhedra. “Polyhedra” is a Greek word meaning “many faces.” There are five of these, and they are characterized by the fact that each face is a regular polygon, that is, a straight-sided figure with equal sides and equal angles:

Tetrahedron 4 Faces 4 Vertices 6 Edges

Cube 6 Faces 8 Vertices 12 Edges

Octahedron 8 Faces 6 Vertices 12 Edges

Dodecahedron 12 Faces 20 Vertices 30 Edges

Icosahedron 20 Faces 12 Vertices 30 Edges

The elements linked to the Platonic Solids
Plato associates four of the Platonic Solid with the four elements. He writes: “We must proceed to distribute the figures [the solids] we have just described between fire, earth, water, and air. . . Let us assign the Cube to earth, for it is the most immobile of the four bodies and most retentive of shape the least mobile of the remaining figures (Icosahedron) to water the most mobile (Tetrahedron) to fire the intermediate (Octahedron) to air Note that earth is associated with the cube, with its six square faces. This lent support to the notion of the foursquaredness of the earth.

Platonic Solids in Art Many painters have used platonic solids in their paintings. Some of them are Leonardo Da Vinci, Albert Durer, Lucas Pacioli, Escher, Salvador Dali and others.

Leonardo Da Vinci

Salvador Dali Sacrament of the Last Supper Christ Crucified

Luca Pacioli JACOPO DE 'BARBERI

Escher

Miriam Escofet the five platonic solids

Kepler Model of Universe

Durer St Jerome in his Study Melancholia