Elongated triangular tiling

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 which describes the corners or intersections of geometric shapes. Vertices are commonly used in computer graphics to define the corners of surfaces in 3D models, where each such point is given as a vector.-Of an angle:The vertex of an angle is the...

.

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 Euclidean plane.

This tiling is related to the snub square tiling

Snub square tiling

In geometry, the snub square tiling is a semiregular tiling of the Euclidean plane. There are three triangles and two squares on each vertex. It has Schläfli symbol of s{4,4}....

 which also has 3 triangles and two squares on a vertex, but in a different order.

This 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 :...

.

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 which describes the corners or intersections of geometric shapes. Vertices are commonly used in computer graphics to define the corners of surfaces in 3D models, where each such point is given as a vector.-Of an angle:The vertex of an angle is the...

.

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 Euclidean plane.

This tiling is related to the snub square tiling

Snub square tiling

In geometry, the snub square tiling is a semiregular tiling of the Euclidean plane. There are three triangles and two squares on each vertex. It has Schläfli symbol of s{4,4}....

 which also has 3 triangles and two squares on a vertex, but in a different order.

This 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.

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.