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.
C1a33.42; 32.4.3.4]1C2a2

Dual tilings

The dual tilings have right triangle and kite faces, defined by face configurations: V3.3.3.4.4 and V3.3.4.3.4, and can be seen combining the prismatic pentagonal tiling and Cairo pentagonal tilings.