A Platonic Polyhedron has the following basic properties:

    All faces are congruent (identical) planar regular convex polygons: equilateral triangles, squares or regular pentagons;

    All vertex figures are congruent (identical) and regular

Tetrahedron Cube Octahedron Dodecahedron Icosahedron

There are five and only five regular convex polyhedra. They are known as Platonic figures, after Plato, who became famous for his elaboration on them, although was not the first one to deal with them.

Each regular polyhedron possesses perfect symmetry as well many other interesting properties. In addition their are mutual relationships between pairs of them and many other interconnections exist among them.  The set of Platonic figures have sparked the imagination of generations of scientists and artists such as Euclid, Kepler, Coxeter, Buckminster Fuller, Escher and many others. 

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