# 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
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octahedron
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( 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.