Prismatic pentagonal tiling

Elongated triangular tiling
Type	Dual uniform tiling
Faces	irregular pentagons
Coxeter diagram
Symmetry group	cmm, [∞,2+,∞], (2*22)
Rotation group	p2, [∞,2,∞]+, (2222)
Dual polyhedron	Elongated triangular tiling
Face configuration	V3.3.3.4.4
Properties	face-transitive

In geometry, the elongated triangular tiling is a semiregular tiling of the Euclidean plane. There are three triangles and two squares on each vertex. It is named as a triangular tiling elongated by rows of squares, and given Schläfli symbol {3,6}:e.

Conway calls it a isosnub quadrille.

There are 3 regular and 8 semiregular tilings in the plane. This tiling is similar to the snub square tiling which also has 3 triangles and two squares on a vertex, but in a different order.

It is also the only uniform tiling that can't be created as a Wythoff construction. It can be constructed as alternate layers of apeirogonal prisms and apeirogonal antiprisms.

There is one uniform colorings of an elongated triangular tiling. Two 2-uniform colorings have a single vertex figure, 11123, with two colors of squares, but are not 1-uniform, repeated either by reflection or glide reflection, or in general each row of squares can be shifted around independently. The 2-uniform tilings are also called Archimedean colorings. There are infinite variations of these Archimedean colorings by arbitrary shifts in the square row colorings.

The elongated triangular tiling can be used as a circle packing, placing equal diameter circles at the center of every point. Every circle is in contact with 5 other circles in the packing (kissing number).

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Wikipedia