# 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:

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

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

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

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

A convex polyhedron bounded by faces of more than one type of regular polygon, with all edges the same length and all vertices identical is called an Archimedean solid. There are 13 Archimedean solids, shown below:

truncated tetrahedron:

4 hexagon + 4 triangle faces

12 vertices, 18 edgestruncated cube:

6 octagon + 8 triangle faces

24 vertices, 36 edgestruncated octahedron:

8 hexagon + 6 square faces

24 vertices, 36 edgestruncated dodecahedron:

12 decagon + 20 triangular faces

60 vertices, 90 edgestruncated icosahedron:

20 hexagon + 12 pentagon faces

60 vertices, 90 edgescuboctahedron:

8 triangle + 6 square faces

12 vertices, 24 edgesrhombicuboctahedron:

18 square + 8 triangle faces

24 vertices, 48 edgestruncated cuboctahedron (or

**great rhombicuboctahedron**):

8 octagon + 8 hexagon + 12 square faces

48 vertices, 72 edgesicosidodecahedron:

20 triangle + 12 pentagon faces

30 vertices, 60 edgesrhombicosidodecahedron:

20 triangle + 30 square + 12 pentagon faces

60 vertices, 120 edgestruncated icosidodecahedron (or

**great rhombicosidodecahedron**):

30 square + 20 hexagon + 12 decagon faces

120 vertices, 180 edgessnub cube:

32 triangle + 6 square faces

24 vertices, 60 edgessnub dodecahedron:

80 triangle + 12 pentagon faces

60 vertices, 150 edges