A regular polyhedron is a polyhedron whose faces are all regular polygons which are identical in both shape and size. Only five regular polyhedrons are possible. These are listed in the table on the right.
There are two particular spheres associated with any regular polyhedron.
First is the circum-sphere This is the sphere which fits around the outside of the polyhedron so as to touch all its vertices (or corners).
Its diameter is given here as the circum-diameter.
Second is the in-sphere This is the sphere which fits inside the polyhedron so as to touch all its faces. Its diameter is given here by the in-diameter.
Polyhedrons are named by the number of faces they have.|
The five regular polyhedrons, and their details, are
The D-angle is the angle (in degrees) between any pair of adjacent faces. This is known as the dihedral angle.
|Name||faces|| ||vertices||edges|| ||D-angle|
|tetrahedron||4|| ||4||6|| ||70.533|
|cube||6|| ||8||12|| ||90|
|octahedron||8|| ||6||12|| ||109.467|
|dodecahedron||12|| ||20||30|| ||116.565|
|icosahedron||20|| ||12||30|| ||138.190|