Snub hexagonal tiling
Encyclopedia
In geometry
, the Snub hexagonal tiling (or snub trihexagonal tiling) is a semiregular tiling of the Euclidean plane. There are four triangles and one hexagon on each vertex
. It has Schläfli symbol of s{3,6}.
Conway
calls it a snub hexatille, constructed as a snub
operation applied to a hexagonal tiling (hexatille).
There are 3 regular and 8 semiregular tilings in the plane. This is the only one which does not have a reflection as a symmetry.
polyhedra with vertex figure (3.3.3.3.p) and Coxeter-Dynkin diagram
. These face-transitive figures have (n32) rotational symmetry.
There is only one uniform coloring
of a snub hexagonal tiling. (Naming the colors by indices (3.3.3.3.6): 11213.)
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 Snub hexagonal tiling (or snub trihexagonal tiling) is a semiregular tiling of the Euclidean plane. There are four triangles and one hexagon 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:...
. It has Schläfli symbol of s{3,6}.
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 snub hexatille, constructed as a snub
Snub (geometry)
In geometry, an alternation is an operation on a polyhedron or tiling that removes alternate vertices. Only even-sided polyhedra can be alternated, for example the zonohedra. Every 2n-sided face becomes n-sided...
operation applied to a hexagonal tiling (hexatille).
There are 3 regular and 8 semiregular tilings in the plane. This is the only one which does not have a reflection as a symmetry.
Related polyhedra and tilings
This tiling is part of sequence of snubbedSnub (geometry)
In geometry, an alternation is an operation on a polyhedron or tiling that removes alternate vertices. Only even-sided polyhedra can be alternated, for example the zonohedra. Every 2n-sided face becomes n-sided...
polyhedra with vertex figure (3.3.3.3.p) and Coxeter-Dynkin diagram
Coxeter-Dynkin diagram
In geometry, a Coxeter–Dynkin diagram is a graph with numerically labeled edges representing the spatial relations between a collection of mirrors...
. These face-transitive figures have (n32) rotational symmetry.
 (3.3.3.3.3) Icosahedron In geometry, an icosahedron is a regular polyhedron with 20 identical equilateral triangular faces, 30 edges and 12 vertices. It is one of the five Platonic solids.... (332) |
 (3.3.3.3.4) Snub cube In geometry, the snub cube, or snub cuboctahedron, is an Archimedean solid.The snub cube has 38 faces, 6 of which are squares and the other 32 are equilateral triangles. It has 60 edges and 24 vertices. It is a chiral polyhedron, that is, it has two distinct forms, which are mirror images of each... (432) |
 (3.3.3.3.5) Snub dodecahedron In geometry, the snub dodecahedron, or snub icosidodecahedron, is an Archimedean solid, one of thirteen convex isogonal nonprismatic solids constructed by two or more types of regular polygon faces.... (532) |
 3.3.3.3.6 (632) |
 3.3.3.3.7 (732) |
 3.3.3.3.8 (832) |
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 a snub hexagonal tiling. (Naming the colors by indices (3.3.3.3.6): 11213.)