.
Wythoff constructions from hexagonal and triangular tilings Like the
uniform polyhedra there are eight
uniform tilings that can be based from the regular hexagonal tiling (or the dual
triangular tiling). Drawing the tiles colored as red on the original faces, yellow at the original vertices, and blue along the original edges, there are 8 forms, 7 which are topologically distinct. (The
truncated triangular tiling is topologically identical to the hexagonal tiling.)
Symmetry mutations This tiling is topologically related as a part of sequence of uniform
truncated polyhedra with
vertex configurations (3.2n.2n), and [n,3]
Coxeter group symmetry.
Related 2-uniform tilings Two
2-uniform tilings are related by dissected the
dodecagons into a central hexagonal and 6 surrounding triangles and squares.
Circle packing The truncated hexagonal tiling can be used as a
circle packing, placing equal diameter circles at the center of every point. Every circle is in contact with 3 other circles in the packing (
kissing number). This is the lowest density packing that can be created from a uniform tiling. :
Triakis triangular tiling ,
China The
triakis triangular tiling is a tiling of the Euclidean plane. It is an equilateral
triangular tiling with each triangle divided into three obtuse triangles (angles 30-30-120) from the center point. It is labeled by
face configuration V3.12.12 because each isosceles triangle face has two types of vertices: one with 3 triangles, and two with 12 triangles.
Conway calls it a
kisdeltille, constructed as a
kis operation applied to a
triangular tiling (deltille). In Japan the pattern is called
asanoha for
hemp leaf, although the name also applies to other triakis shapes like the
triakis icosahedron and
triakis octahedron. It is the dual tessellation of the truncated hexagonal tiling which has one triangle and two dodecagons at each vertex. : It is one of eight
edge tessellations, tessellations generated by reflections across each edge of a prototile.
Related duals to uniform tilings It is one of 7 dual uniform tilings in hexagonal symmetry, including the regular duals. == See also ==