Both Platonic Solids and Archimedean Solids can be described by their vertex configurations as well as their number of vertices, edges, and faces. A vertex configuration lists the number of sides of each regular polygon that meets at each vertex, in the order that they appear. For example, a vertex configuration of (3.4.3) refers to a vertex contained by a triangle, square, and triangle in that order.
Note that each Archimedean Solid can be made from applying certain operations to the Platonic Solids.