Platonic Solid

In Euclidean geometry, a Platonic solid is a regular, convex polyhedron. The faces are congruent, regular polygons, with the same number of faces meeting at each vertex. There are exactly five solids which meet those criteria; each is named according to its number of faces.

Tetrahedron
(four faces)
Cube or hexahedron
(six faces)
Octahedron
(eight faces)
Dodecahedron
(twelve faces)
Icosahedron
(twenty faces)





The aesthetic beauty and symmetry of the Platonic solids have made them a favorite subject of geometers for thousands of years. They are named for the ancient Greek philosopher Plato, who theorized that the classical elements were constructed from the regular solids.

Read more about Platonic Solid:  History, Combinatorial Properties, Classification, In Nature and Technology

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Platonic Solid - Related Polyhedra and Polytopes - Higher Dimensions
... being the equivalents of the three-dimensional Platonic solids ... Schläfli discovered the four-dimensional analogues of the Platonic solids, called convex regular 4-polytopes ... There are exactly six of these figures five are analogous to the Platonic solids, while the sixth one, the 24-cell, has one lower-dimension analogue (Truncation of a simplex-fac ...

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