(arranged in the order that they might be encountered in the study of polyhedra)
A regular polygon is a polygon which is equilateral and equiangular.
A regular polyhedron is a polyhedron whose sides are all the same regular polygonal shape and whose vertices all form the same angle.
The Platonic Solids are the 5 convex regular polyhedron; tetrahedron, hexahedron, octahedron, dodecahedron, and icosahedron. They were named for the Greek philosopher, Plato, because he believed that these shapes were the substance of all matter.
The Archimedian Solids are polyhedron that are made from two or more regular polygonal faces. Each of their vertices are identical consisting of the conjunction of identical groups of polygons.
The Archimedian Solids were named after the Greek mathematician and engineer, Archimedes, who first described them.
There are 13 Archimedian Solids.
A truncated polyhedron is a polyhedron whose vertices as well as some part of the polyhedron appears to have been "sliced off".
Quasi-regular polyhedra are polyhedra that are composed of only two different regular faces. However, one of those kinds of faces is always completely surrounded by the other regular face.
A compound polyhedron Is a polyhedron made up of two or more polyhedra that share the same central point and seem to pass through each other.
Enantiomorphous In creating polyhedra, it often happens that one-half of a polyhedron is the mirror image of the other half of that polyhedron. All of the pieces of that one-half polyhedron are adjacent to the same pieces as the other half of the polyhedron but are joined in opposite directions. These two halves are said to be enantiomorphic.
Rhombic polyhedra are polyhedra that contain extra square faces.
Stellated polyhedra are polyhedra that have had their faces or edges extended to form a new polyhedral shape that is called stellated. Stellated polyhedra are star-like.