Order-8 triangular tiling

It is represented by Schläfli symbol of {3,8}, having eight regular triangles around each vertex.

The half symmetry [1+,8,3] = [(4,3,3)] can be shown with alternating two colors of triangles: From [(4,4,4)] symmetry, there are 15 small index subgroups (7 unique) by mirror removal and alternation operators.

Adding 3 bisecting mirrors across each fundamental domains creates 832 symmetry.

A larger subgroup is constructed [(4,4,4*)], index 8, as (2*2222) with gyration points removed, becomes (*22222222).

From a Wythoff construction there are ten hyperbolic uniform tilings that can be based from the regular octagonal and order-8 triangular tilings.