Platonic Polyhedra

The Platonic solids were named after Plato. Plato did not discover Platonic polyhedra, but he and his followers studied them extensively. Platonic polyhedra are often called regular polyhedra.

There are only five Platonic polyhedra. Each Platonic polyhedron is convex, and there are an equal number of regular, convex faces meeting at each of its vertices. There are only five of these figures because at least three faces must meet at each vertex to create a three-dimensional object, and the sum of the face angles around that vertex must be less than 360 degrees or else the surface will be flat or concave.

Tetrahedron

The Tetrahedron has four faces. Three faces meet at each of its four vertices. Each face is an equilateral triangle.

Hexahedron

The Hexahedron has four faces. Three faces meet at each of its eight vertices. Each face is a square.

Octahedron

The Octahedron has eight faces. Four faces meet at each of its six vertices. Each face is an equilateral triangle.

Icosahedron

The Icosahedron has twenty faces. Five faces meet at each of its twelve vertices. Each face is an equilateral triangle.

Dodecahedron (Pentagonal Dodecahedron)

The Dodecahedron has twelve faces. Three faces meet at each of its twenty vertices. Each face is a regular pentagon.

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