Some Monohedral Tilings Derived From Regular Polygons

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Paul Gailiunas: Some Monohedral Tilings Derived From Regular Polygons. In: Bridges 2007. Pages 9–14



Some tiles derived from regular polygons can produce spiral tilings of the plane [1]. This paper considers some more general classes of tilings with tiles derived from regular polygons, some have central symmetry, many have periodic symmetry, some have both, and a few have no symmetry at all. Any of these tiling patterns could be the basis for some interesting mathematical art, for example by colouring or decorating the tiles.

Extended Abstract


Used References

[1] Gailiunas P., "Spiral Tilings" Bridges 2000, pp.133-140.

[2] US Patent 4,620,998, 1986, cited in Lalvani H., Meta Archtecture, in Architecture and Science (ed. Di Cristina G.), Wiley Academy, 2001.

[3] Stock D.L. and Wichmann B.A., "Odd Spiral Tilings", Mathematics Magazine vol.73, no.5, Dec 2000, pp.339-347.

[4] Hatch G. "Tessellations with Equilateral Reflex Polygons", Mathematics Teaching, no.84, Sept.1978, p.32.

[5] Simonds D.R., "Central Tessellations with an Equilateral Pentagon", Mathematics Teaching, no.81, Dec. 1977, p.36.

[6] Grünbaum B., and Shephard G.C., "Spiral Tilings and Versatiles", Mathematics Teaching, no.88, Sept. 1979, pp.50−1.

[7] Rice M. and Schattschneider D., "The Incredible Pentagonal Versatile", Mathematics Teaching, no.93, Dec. 1980, pp.52−3.


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