Tiling with Regular Polygons and Rhombs

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Kevin Jardine: Imperfect Congruence: Tiling with Regular Polygons and Rhombs. In: Bridges 2013. Pages 439–442



Edge-to-edge plane tilings of regular polygons can include only squares, triangles, hexagons, octagons, and dodecagons. The possibilities become far larger, striking and beautiful if we add rhombs to the prototile set.

Extended Abstract


Used References

[1] Johannes Kepler. Translated by E. J. Aiton, Alistair Matheson Duncan, and Judith Veronica Field. The Harmony of the World. American Philosophical Society, 1997.

[2] Duncan M. Y. Sommerville.“Semi-regular Networks of the Plane in Absolute Geometry”, Transactions of the Royal Society of Edinburgh, 41, pp 725-747, 1906.

[3] Kevin Jardine. Imperfect Congruence website. http://gruze.org/tilings (as of March 5, 2013).

[4] Sampath Kannan and Danny Soroker. “Tiling polygons with parallelograms”, Discrete & Computational Geometry, Volume 7, Issue 1, pp 175-188, 1992.

[5] Richard Kenyon.“Tiling a polygon with parallelograms”, Algorithmica, Volume 9, Issue 4, pp 382-397, April 1993.


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