An actual truncation of the trihexagonal tiling has rectangles instead of squares, and its hexagonal and dodecagonal faces can not both be regular.

(Compare the disdyakis hexa-, dodeca- and triacontahedron, three Catalan solids similar to this tiling.)

Conway calls it a kisrhombille[1] for his kis vertex bisector operation applied to the rhombille tiling.

(Alternately it can be seen as a bisected triangular tiling divided into 6 triangles, or as an infinite arrangement of lines in six parallel families.)

The kisrhombille tiling triangles represent the fundamental domains of p6m, [6,3] (*632 orbifold notation) wallpaper group symmetry.

There are a number of small index subgroups constructed from [6,3] by mirror removal and alternation.

This tiling can be considered a member of a sequence of uniform patterns with vertex figure (4.6.2p) and Coxeter-Dynkin diagram .