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:

Circle Packings
These 2-uniform tilings can be used as a circle packings.

In the first 2-uniform tiling (whose dual resembles a key-lock pattern): cyan circles are in contact with 5 other circles (3 cyan, 2 pink), corresponding to the V33.42 planigon, and pink circles are also in contact with 5 other circles (4 cyan, 1 pink), 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 (mini-vertex configuration polygons; one dimensional duals to the respective planigons). Both images coincide.

In the second 2-uniform tiling (whose dual resembles jagged streams of water): cyan circles are in contact with 5 other circles (2 cyan, 3 pink), corresponding to the V33.42 planigon, and pink circles are also in contact with 5 other circles (3 cyan, 2 pink), 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 (mini-vertex configuration polygons; one dimensional duals to the respective planigons). Both images coincide.

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.