Equitransitive edge-to-edge tilings by regular convex polygons

@article{Debroey1981EquitransitiveET,
  title={Equitransitive edge-to-edge tilings by regular convex polygons},
  author={I. Debroey and Françoise Landuyt},
  journal={Geometriae Dedicata},
  year={1981},
  volume={11},
  pages={47-60}
}
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

Tilings by Regular Polygons
A tiling of the plane is a family of sets called tiles that cover the plane without gaps or overlaps. ("Without overlaps" means that the intersection of any two of the sets has measure (area) zero.)Expand