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Tilings are two dimensional tesselations. They are the most widely studied variety of tesselation, and there are many many resources you can find on the intricacies of plane tiling. However, despite all of the attention the plane gets, there has yet to be a proof of completeness of the uniform tilings. Thus, this list of 53 may not be complete. Note that we do not include the apeirogonal dihedron or its dual, as they are not faithful. This page is based off of Eric Binnendyk's old one.
Category 1: Regulars (Tilings 1 - 3) - Contains the three regular Euclidean tilings, the square, triangular, and hexagonal tilings. These should be very familiar.
Category 2: Truncates (Tilings 4 - 7) - Contains the 2 truncates and 2 quasitruncates of regular Euclidean tilings. Hexat has subsymmetry of this type.
Category 3: Quasiregulars (Tilings 8 - 12) - Contains 2 bonus demi-symmetric members of regulars, as well as the one rectate regiment of three, that.
Category 4: Trapeziverts (Tilings 13-24) - Contains 4 regiments of three, the colonels have trapezoidal vertex figures. That and squat have subsymmetry of this type.
Category 5: Omnitruncates (Tilings 25-30) - These 6 have scalene triangles as verfs. Hexat has subsymmetry of this type.
Category 6: Snubs (Tilings 31-34) - These 4 are the "standard" snub tilings, derivable as alternated omnitruncates. Two of these have doubled symmetry.
Category 7: Laminates (Tilings 35-38) - This category contains the apeirogonal prism and antiprism, and two tilings formed by blending them. Azip and azap could technically go in category 2 and 6 respectively, but they're here for convenience.
Category 8: Other Blends (Tilings 39-53) - This category contains tilings that are formed by blending other tilings in more complicated ways. Two of these are based on the laminates, six are based on sossa's superregiment, six are based on shaha's superregiment, and the last one has an odd construction with strange chiral cyclotriangular symmetry.
Here are other pages on uniform tilings. Only the Wikipedia page has an up-to-date list.
Mandara - The World of Uniform Tessellations by Hironori Sakamoto. This site has probably the best graphics, but is missing the ionic sossas from category 8. Many interesting hyperbolics are here too.
Dr. Richard Klitzing's page on Euclidean tesellations. Contains mostly just wythoffians.
Uniform tiling on Wikipedia.
Site by Benjamin Klein
contact me via emailbenklein at gmail dot com or on the Polytope Discord