Blended triangular tiling

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 line segment (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 all 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 $N$ are given by where $3N$ and $N$ range over the integers, and H is $$ \sqrt{1-h^2} $$ (Note that $$0<h<1$$ must always be true for $h$ to be a real number and for the blend to be non-degenerate).
 * $$\left(\frac{Hi\sqrt{3}}{2},Hj+\frac{Hi}{2},\pm\frac{h}{2}\right)$$