In geometry

Geometry

Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....

, the elongated triangular tiling is a semiregular tiling

Tiling by regular polygons

Plane tilings by regular polygons have been widely used since antiquity. The first systematic mathematical treatment was that of Kepler in Harmonices Mundi.- Regular tilings :...

 of the Euclidean plane. There are three triangles and two squares on each vertex

Vertex (geometry)

In geometry, a vertex is a special kind of point that describes the corners or intersections of geometric shapes.-Of an angle:...

.

Conway

John Horton Conway

John Horton Conway is a prolific mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory...

 calls it a isosnub quadrille.

There are 3 regular and 8 semiregular tilings in the plane. This tiling is related 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

Uniform tiling

In geometry, a uniform tiling is a tessellation of the plane by regular polygon faces with the restriction of being vertex-uniform.Uniform tilings can exist in both the Euclidean plane and hyperbolic plane...

 that can't be created as a Wythoff construction

Wythoff construction

In geometry, a Wythoff construction, named after mathematician Willem Abraham Wythoff, is a method for constructing a uniform polyhedron or plane tiling. It is often referred to as Wythoff's kaleidoscopic construction.- Construction process :...

. It can be constructed as alternate layers of apeirogonal prism

Apeirogonal prism

In geometry, an apeirogonal prism or infinite prism is the arithmetic limit of the family of prisms; it can be considered an infinite polyhedron or a tiling of the plane....

s and apeirogonal antiprism

Apeirogonal antiprism

In geometry, an apeirogonal antiprism or infinite antiprism is the arithmetic limit of the family of antiprisms; it can be considered an infinite polyhedron or a tiling of the plane.If the sides are equilateral triangles, it is a uniform tiling...

s.

Uniform colorings

There is only one uniform coloring

Uniform coloring

In geometry, a uniform coloring is a property of a uniform figure that is colored to be vertex-transitive...

of an elongated triangular tiling. (Naming the colors by indices around a vertex (3.3.3.4.4): 11122.) A second nonuniform coloring 11123 also exists. The coloring shown is a mixture of 12134 and 21234 colorings.