Dual Tessellation
The dual of a regular tessellation is formed by taking the center of each polygon as a vertex and joining the centers of adjacent polygons.
DualTessellations
The triangular and hexagonal tessellations are duals of each other, while the square tessellation it its own dual.
DualSemiregularTess
Williams (1979, pp. 37-41) illustrates the dual tessellations of the semiregular tessellations.
See also
Cairo Tessellation, TessellationExplore with Wolfram|Alpha
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References
Wells, D. The Penguin Dictionary of Curious and Interesting Geometry. London, England: Penguin, pp. 60-61, 1991.Williams, R. The Geometrical Foundation of Natural Structure: A Source Book of Design. New York: Dover, p. 37, 1979.Referenced on Wolfram|Alpha
Dual TessellationCite this as:
Weisstein, Eric W. "Dual Tessellation." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/DualTessellation.html