\begin{definition}[Definition:Archimedean Polyhedron]
An '''Archimedean polyhedron''' is a convex polyhedron with the following properties:
:$(1): \quad$ Each of its faces is a regular polygon
:$(2): \quad$ It is vertex-transitive
:$(3): \quad$ The faces are not all congruent.
:$(4): \quad$ It is not a regular prism or a regular antiprism.
\end{definition}