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A Polyhedron or plane Tessellation is called semiregular if its faces are all Regular Polygons and its corners are alike (Walsh 1972; Coxeter 1973, pp. 4 and 58; Holden 1991, p. 41). The usual name for a semiregular polyhedron is an Archimedean Solid, of which there are exactly 13.
See also Archimedean Solid, Polyhedron, Tessellation
References
Coxeter, H. S. M. ``Regular and Semi-Regular Polytopes I.'' Math. Z. 46, 380-407, 1940.
Coxeter, H. S. M. Regular Polytopes, 3rd ed. New York: Dover, 1973.
Holden, A. Shapes, Space, and Symmetry. New York: Dover, 1991.
Walsh, T. R. S. ``Characterizing the Vertex Neighbourhoods of Semi-Regular Polyhedra.''
Geometriae Dedicata 1, 117-123, 1972.