Regular tessellations of the plane by two or more convex regular polygons such that the same polygons in the same order surround each polygon vertex are called semiregular tessellations, or sometimes Archimedean tessellations. In the plane, there are eight such tessellations, illustrated above (Ghyka 1977, pp. 76-78; Williams 1979, pp. 37-41; Steinhaus 1999, pp. 78-82; Wells 1991, pp. 226-227). Williams (1979, pp. 37-41) also illustrates the dual tessellations of the semiregular tessellations. The dual tessellation of the tessellation of squares and equilateral triangles is called the Cairo tessellation (Williams 1979, p. 38; Wells 1991, p. 23).
Semiregular Tessellation
See also
Cairo Tessellation, Demiregular Tessellation, Regular Tessellation, Semiregular Polyhedron, TessellationExplore with Wolfram|Alpha
References
Ghyka, M. C. The Geometry of Art and Life, 2nd ed. New York: Dover, 1977.Steinhaus, H. Mathematical Snapshots, 3rd ed. New York: Dover, 1999.Wells, D. The Penguin Dictionary of Curious and Interesting Geometry. London: Penguin, 1991.Williams, R. The Geometrical Foundation of Natural Structure: A Source Book of Design. New York: Dover, 1979.Referenced on Wolfram|Alpha
Semiregular TessellationCite this as:
Weisstein, Eric W. "Semiregular Tessellation." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SemiregularTessellation.html