# List of uniform tilings

. . . Uniform honeycombs

Welcome to my website on uniform tilings of 2D Euclidean space.

## What is a uniform tiling?

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.

## Uniform tiling categories

**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."

## Other pages

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