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Great rhombitrihexagonal tiling

 

 
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Great rhombitrihexagonal tiling
 
 
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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 Great rhombitrihexagonal tiling (or Omnitruncated trihexagonal tiling) is a semiregular tiling of the Euclidean plane. There are one square, one hexagon, and one dodecagon (12-sides) 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....
. It has Schläfli symbol
Schläfli symbol

In mathematics, the Schl?fli symbol is a notation of the form that defines regular polytopes and tessellations.The Schl?fli symbol is named after the 19th-century mathematician Ludwig Schl?fli who made important contributions in geometry and other areas....
 of t0,1,2.

Conway
John Horton Conway

John Horton Conway is a prolific mathematician active in the theory of finite group , knot theory, number theory, combinatorial game theory and coding theory....
 calls it a truncated hexadeltille, constructed as a truncation
Truncation (geometry)

In geometry, a truncation is an operation in any dimension that cuts polytope vertices, creating a new Facet in place of each vertex....
 operation applied to a trihexagonal tiling
Trihexagonal tiling

In geometry, the trihexagonal tiling is a semiregular tiling of the Euclidean plane. There are two triangles and two hexagons alternating on each vertex ....
 (hexadeltille).

There are 3 regular and 8 semiregular tilings in the plane.

This tiling is topologically related as a part of sequence of omnitruncated
Omnitruncation (geometry)

In geometry, an omnitruncation is an operation applied to a regular polytope in a Wythoff construction that creates a maximum number of facets....
 polyhedra with vertex figure (4.6.2p) and Coxeter-Dynkin diagram
Coxeter-Dynkin diagram

In geometry, a Coxeter-Dynkin diagram is a Graph with labelled edges. It represents the spatial relations between a collection of mirrors , and describes a Kaleidoscope construction....
 .






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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 Great rhombitrihexagonal tiling (or Omnitruncated trihexagonal tiling) is a semiregular tiling of the Euclidean plane. There are one square, one hexagon, and one dodecagon (12-sides) 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....
. It has Schläfli symbol
Schläfli symbol

In mathematics, the Schl?fli symbol is a notation of the form that defines regular polytopes and tessellations.The Schl?fli symbol is named after the 19th-century mathematician Ludwig Schl?fli who made important contributions in geometry and other areas....
 of t0,1,2.

Conway
John Horton Conway

John Horton Conway is a prolific mathematician active in the theory of finite group , knot theory, number theory, combinatorial game theory and coding theory....
 calls it a truncated hexadeltille, constructed as a truncation
Truncation (geometry)

In geometry, a truncation is an operation in any dimension that cuts polytope vertices, creating a new Facet in place of each vertex....
 operation applied to a trihexagonal tiling
Trihexagonal tiling

In geometry, the trihexagonal tiling is a semiregular tiling of the Euclidean plane. There are two triangles and two hexagons alternating on each vertex ....
 (hexadeltille).

There are 3 regular and 8 semiregular tilings in the plane.

This tiling is topologically related as a part of sequence of omnitruncated
Omnitruncation (geometry)

In geometry, an omnitruncation is an operation applied to a regular polytope in a Wythoff construction that creates a maximum number of facets....
 polyhedra with vertex figure (4.6.2p) and Coxeter-Dynkin diagram
Coxeter-Dynkin diagram

In geometry, a Coxeter-Dynkin diagram is a Graph with labelled edges. It represents the spatial relations between a collection of mirrors , and describes a Kaleidoscope construction....
 . The following forms exist as tilings of the hyperbolic plane, starting with the great rhombitriheptagonal tiling
Great rhombitriheptagonal tiling

In geometry, the great rhombitrihexagonal tiling is a semiregular tiling of the Euclidean plane. There are one square, one hexagon, and one tetrakaidecagon on each vertex ....
. This set of polyhedra are zonohedron
Zonohedron

A zonohedron is a convex set polyhedron where every face is a polygon with point symmetry or, equivalently, symmetry under rotations through 180?....
s.

Uniform Polyhedron 23 T01

(4.6.4)
Hexagonal prism

In geometry, the hexagonal prism is a Prism with hexagonal base.It is an octahedron. However, the term octahedron is mainly used with "regular" in front or implied, hence not meaning a hexagonal prism; in the general meaning the term octahedron it is not much used because there are different types which have not much in common exce...


(4.6.6)
Truncated octahedron

The truncated octahedron is an Archimedean solid. It has 8 regular hexagonal faces, 6 Square faces, 24 vertices and 36 edges. Since each of its faces has point symmetry the truncated octahedron is a zonohedron....


(4.6.8)

(4.6.10)
Uniform Polyhedron 63 T012

(4.6.12)

(4.6.14)
Great rhombitriheptagonal tiling

In geometry, the great rhombitrihexagonal tiling is a semiregular tiling of the Euclidean plane. There are one square, one hexagon, and one tetrakaidecagon on each vertex ....


(4.6.16)


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. Different Symmetry can be expressed on the same geometric figure with the Face following different uniform color patterns....
s of a Great rhombitrihexagonal tiling. (Naming the colors by indices around a vertex: 123.)

See also

  • Tilings of regular polygons
  • List of uniform tilings


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