. . . Uniform honeycombs
Welcome to my website on uniform tilings of 2D Euclidean space.
The formal definition of a uniform tiling is similar to the formal definition of a uniform honeycomb, but one dimension lower. A tiling is an abstract polyhedron embedded in 2-space. It is strictly connected, dyadic, non-coincidic, and monal. A uniform tiling is a vertex-transitive tiling whose faces are all regular polygons or apeirogons.
Category 1: Regulars - Contains the three regular Euclidean tilings.
Category 2: Truncates - Contains the truncates and quasitruncates of regular Euclidean tilings.
Category 3: Quasiregulars - Contains regiments of regulars and rectates, excluding rectates themselves.
Category 4: Trapeziverts - Contains tilings with trapezoidal vertex figures and their regiments.
Category 5: Omnitruncates - These have scalene triangles as verfs.
Category 6: Snubs - These are the "standard" snub tilings, derivable as alternated omnitruncates.
Category 7: Layered tilings - This category contains the apeirogonal prism and antiprism, and two tilings formed by blending them.
Category 8: Other blends - This category contains tilings that are formed by blending other tilings in a more complicated way. These tilings were originally published on a Japanese webpage under the name "complex uniform tesellations."
Here are other people's pages on similar polytopes.
Mandara - The World of Uniform Tessellations by "hsaka"
Dr. Richard Klitzing's page on Euclidean tesellations
Uniform tiling from Wikipedia