33344-33434 tiling
In geometry of the Euclidean plane, a 33344-33434 tiling is one of two of 20 2-uniform tilings of the Euclidean plane by regular polygons. They contains regular triangle and square faces, arranged in two vertex configuration: 3.3.3.4.4 and 3.3.4.3.4.
The first has triangles in groups of 3 and square in groups of 1 and 2. It has 4 types of faces and 5 types of edges.
The second has triangles in groups of 4, and squares in groups of 2. It has 3 types of face and 6 types of edges.
Geometry
Its two vertex configurations are shared with two 1-uniform tilings:3.3.4.3.4 | 3.3.3.4.4 |
snub square tiling | elongated triangular tiling |
Circle Packings
These 2-uniform tilings can be used as a circle packings.In the first 2-uniform tiling : cyan circles are in contact with 5 other circles, corresponding to the V33.42 planigon, and pink circles are also in contact with 5 other circles, corresponding to the V32.4.3.4 planigon. It is homeomorphic to the ambo operation on the tiling, with the cyan and pink gap polygons corresponding to the cyan and pink circles. Both images coincide.
In the second 2-uniform tiling : cyan circles are in contact with 5 other circles, corresponding to the V33.42 planigon, and pink circles are also in contact with 5 other circles, corresponding to the V32.4.3.4 planigon. It is homeomorphic to the ambo operation on the tiling, with the cyan and pink gap polygons corresponding to the cyan and pink circles. Both images coincide.
| C1 | a33.42; 32.4.3.4]1 | C2 | a2 |