Sphinx tiling

Four 'sphinx' hexiamonds can be put together to form another sphinx.

In geometry, the sphinx tiling is a tessellation of the plane using the "sphinx", a pentagonal hexiamond formed by gluing six equilateral triangles together. The resultant shape is named for its reminiscence to the Great Sphinx at Giza. A sphinx can be dissected into any square number of copies of itself,^[1] some of them mirror images, and repeating this process leads to a non-periodic tiling of the plane. The sphinx is therefore a rep-tile (a self-replicating tessellation).^[2] It is one of few known pentagonal rep-tiles and is the only known pentagonal rep-tile whose sub-copies are equal in size.^[3]

Dissection of the sphinx into four sub-copies

Dissection of the sphinx into nine sub-copies

References

↑ Niţică, Viorel (2003), "Rep-tiles revisited", MASS selecta, Providence, RI: American Mathematical Society, pp. 205–217, MR 2027179 .
↑ Godrèche, C. (1989), "The sphinx: a limit-periodic tiling of the plane", Journal of Physics A: Mathematical and General, 22 (24): L1163–L1166, doi:10.1088/0305-4470/22/24/006, MR 1030678
↑ Martin, Andy (2003), "The sphinx task centre problem", in Pritchard, Chris, The Changing Shape of Geometry, MAA Spectrum, Cambridge University Press, pp. 371–378, ISBN 9780521531627

Periodic

Pythagorean Rhombille Schwarz triangle Rectangle Domino Uniform tiling & honeycomb Coloring Convex Kisrhombille Wallpaper group Wythoff

Aperiodic

Ammann–Beenker Aperiodic set of prototiles List Einstein problem Socolar–Taylor Gilbert Penrose Pentagonal Pinwheel Quaquaversal Rep-tile & Self-tiling Sphinx Truchet

Other

Anisohedral & Isohedral Architectonic & catoptric Circle Limit III Computer graphics Honeycomb Isotoxal Packing Problems Domino Wang Heesch's Squaring Prototile Conway criterion Girih Regular Division of the Plane Regular grid Substitution Voronoi Voderberg

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