Polyhedron

A polyhedron is a three-dimensional geometric closed figure bounded by a connected set of polygons. A polyhedron, in Euclidian geometry, must have at least four faces. A polyhedron of four sides is called a tetrahedron, six sides a hexahedron, eight sides an octahedron, ten sides a decahedron. Figures with more sides are typically named with the Greek name for the number of sides, followed by "-hedron".

The polygons bounding a polyhedron are known as faces; the line segments bounding the polygons are known as edges, and the points where the faces meet are vertices (singular vertex).

A convex polyhedron bounded by faces which are all the same-sized regular polygon is known as a Platonic solid. There are only five Platonic solids, shown below:

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  regular tetrahedron:4 triangle faces, 4 vertices, 6 edges

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  cube: 6 square faces, 8 vertices, 12 edges

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  regular octahedron: 8 triangle faces, 6 vertices, 12 edges

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  regular dodecahedron: 12 pentagon faces, 20 vertices, 30 edges

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  regular icosahedron: 20 triangle faces, 12 vertices, 30 edges