Tilings

Some (mostly on-line) resources

Introductory papers, Lecture notes and Survey papers:

• Chaim Goodman-Strauss, Tessellations.
• Federico Ardila, Richard P. Stanley, Tilings.
• David S. Richeson , A Brief History of Tricky Mathematical Tiling.
• Charles Radin, Conway and aperiodic tilings.
• Lorenzo Sadun, Tilings, tilings spaces and topology.
• Chaim Goodman-Strauss, Open questions in tiling.
• Dmitry Fuchs, Serge Tabachnikov, Impossible tilings, Lecture 23, in "Mathematical Omnibus".

Library books:

• Robert J. Lang, Twists, Tilings, and Tessellations.
• Michael Baake, Uwe Grimm, Aperiodic order. Volume 1, A mathematical invitation.
• Robert Fathauer, Tessellations. Mathematics, Art, and Recreation.
• John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things.

Aperiodic tilings:

• B. Durand and A. Shen, An Aperiodic Set of Eleven Wang Tiles (review of E. Jeandel and M. Rao, “An aperiodic set of 11 Wang tiles”).
• Marjorie Senechal, Aperiodic Monotiles.
• Sébastien Labbé, Peter Selinger, A construction of the hat tilings by a Markov partition.

Polyominoes:

• Nick Mackinnon, Some thoughts on polyomino tiles.
• Branko Grünbaum, G. C. Shephard, Idiot-Proof Tiles.
• David R. MacIver, Notes on tiling with polyominoes.

Spherical tilings:

• Robert Dawson Some New Tilings of the Sphere with Congruent Triangles.

Hyperbolic tilings:

• Make Hyperbolic Tilings of Images by Malin Christersson.
• Interactive Hyperbolic Tiling in the Poincaré Disc, by Malin Christersson.
• Silvio Levy Automatic Generation of Hyperbolic Tilings.
• David R. MacIver, Tilings of Hyperbolic Spaces on the Geometry Junkyard by David Eppstein.
• Nicolas Belmonte Hyperbolic Floors.

Some other results:

• John H. Conway, Yang Jiao, and Salvatore Torquato, New family of tilings of three-dimensional Euclidean space by tetrahedra and octahedra.
• Ludwig Danzer, Branko Grünbaum, G. C. Shephard, Equitransitive Tilings, or How to Discover New Mathematics.
• Rebekah Aduddell, Morgan Ascanio, Adam Deaton, Casey Mann, Unilateral and equitransitive tilings by equilateral triangles.
• Andrey Kupavskii, Janos Pach, Gabor Tardos, Tilings with noncongruent triangles.
• Colin Adams, Cameron Edgar, Peter Hollander, Liza Jacoby, The rest of the tilings of the sphere by regular polygons.
• Colin Adams, Spandrelized Tilings. ( Access through Durham University library).
• Richard Kenyon, Families of convex tilings.

Webpages:

• D. Frettlöh, F. Gähler, E. Harriss Tilings Encyclopedia. (Nonperiodic substitution tilings)
• Lists of uniform tilings on the sphere, plane, and hyperbolic plane on Wikipedia.

Some slides:

• Richard P. Stanley Plane Tilings.