# Blended triangular tiling

Blended triangular tiling
Rank3
Dimension3
TypeRegular
SpaceEuclidean
Notation
Schläfli symbol{3,6}#{}
Elements
FacesN  skew triangles
Edges3N
VerticesN
Vertex figureHexagon, 0 < edge length < 1
Petrie polygonsZigzags
HolesSkew hexagons
Related polytopes
ArmyTriangular tilingprism
Dual{6,6 | 2} (degenerate)
Petrie dualPetrial blended triangular tiling
φ 2 Blended hexagonal tiling
Convex hullTriangular tiling prism
Abstract & topological properties
Schläfli type{6,6}
OrientableYes
Genus
Properties
SymmetryV3×A1
ConvexNo
Dimension vector(1,2,2)

The blended triangular tiling is a regular skew polyhedron that contains an infinite number of skew triangles, with 6 at each vertex. It can be obtained by blending the triangular tiling with a dyad (hence the name). It can be represented as the Schläfli symbol {3,6}#{}. The actual height of the blended triangular tiling can vary, however these are ordinarily considered to still be one polyhedron (just like how the skew square can vary in height but it is still considered the same regular polygon).

Unlike the blended square tiling and the blended hexagonal tiling the blended triangular tiling is not abstractly equivalent to its non-blended version.

## Vertex coordinates

Vertex coordinates of a blended triangular tiling centered at the origin with edge length 1 and height h  are given by

• ${\displaystyle \left({\frac {Hi{\sqrt {3}}}{2}},Hj+{\frac {Hi}{2}},\pm {\frac {h}{2}}\right)}$,

where i  and j  range over the integers, and H is ${\displaystyle {\sqrt {1-h^{2}}}}$ (Note that ${\displaystyle 0 must always be true for H  to be a real number and for the blend to be non-degenerate).