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. In addition, a prism or antiprism is considered semiregular if all its faces are regular polygons.
See alsoAntiprism, Archimedean Solid, Polyhedron, Prism, Semiregular Tessellation, Tessellation
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ReferencesCoxeter, 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.
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Weisstein, Eric W. "Semiregular Polyhedron." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SemiregularPolyhedron.html