# Regular polyhedrons

*Regular polygons. Convex regular polyhedrons: tetrahedron,*

hexahedron (cube), octahedron, dodecahedron, icosahedron.

Non-convex regular polyhedrons.

hexahedron (cube), octahedron, dodecahedron, icosahedron.

Non-convex regular polyhedrons.

A *polyhedron* is called a *regular* one, if all its faces are equal regular polygons and the same number of faces join in each its vertex.

It is known only * five* *convex regular polyhedrons *and *four non-convex regular polyhedrons. * The regular convex polyhedrons

are the following: a *tetrahedron* ( 4 faces, Fig.99 ); a *hexahedron *( 6 faces, Fig.100 ) – well known for us as

a *cube*; an *octahedron *( 8 faces, Fig.101 ); a *dodecahedron* (12 faces, Fig.102); an *icosahedron* ( 20 faces, Fig.103 ).

It is possible to inscribe a sphere into any regular polyhedron and to circumscribe a sphere around any regular polyhedron.