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A Platonic solid is a solid all of whose face are regular and congruent polygons.

There are five of these:

A Tetrahedron. Four faces, each an equilateral triangle.

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A Hexahedron (Cube). Six faces, each a square.

An Octahedron. Eight faces, each an equilateral triangle.

A Dodecahedron. Twelve faces, each a regular pentagon.

An Icosahedron. Twenty faces, each an equilateral triangle.

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Q: What makes a solid a regular platonic solid?
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