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Equitransitive edge-to-edge tilings by regular convex polygons

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Abstract

In their article ‘Tilings by regular polygons’, B. Grünbaum and G. C. Shephard [1] conjecture that there are 19 equitransitive edge-to-edge tilings by regular convex polygons. We prove that there are 22 equitransitive edge-to-edge tilings by regular convex polygons, and it turns out that 3 of them are 1-equitransitive, 13 are 2-equitransitive, 5 are 3-equitransitive and 1 is 4-equitransitive.

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References

  1. Grünbaum, B. and Shephard, G. C., ‘Tilings by Regular Polygons’, Math. Mag. 50 (1977), 227–247.

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  2. Grünbaum, B. and Shephard, G. C., Tilings and Patterns. Freeman and Co., to appear.

  3. Grünbaum, B., Private communication (1979).

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Authors and Affiliations

  1. Limburgs Universitair Centrum, Departement WNF, Universitaire Campus, B-3610, Diepenbeek, Belgium

    I. Debroey

  2. Département de Mathématique, Université Libre de Bruxelles, Boulevard du Triomphe, Campus Plaine - C.P.: 216, B-1050, Bruxelles, Belgium

    F. Landuyt

Authors
  1. I. Debroey
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  2. F. Landuyt
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Debroey, I., Landuyt, F. Equitransitive edge-to-edge tilings by regular convex polygons. Geom Dedicata 11, 47–60 (1981). https://doi.org/10.1007/BF00183189

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  • DOI: https://doi.org/10.1007/BF00183189

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