it has five alternated constructions from reflectional coxeter groups all with four mirrors and only the first being regular: [6,3,3], [3,6,3], [6,3,6], [6,3] and [3] , having 1, 4, 6, 12 and 24 times larger fundamental domains respectively. in coxeter notation subgroup markups, they are related as: [6,(3,3)] (remove 3 mirrors, index 24 subgroup); [3,6,3] or [3,6,3] (remove 2 mirrors, index 6 subgroup); [1,6,3,6,1] (remove two orthogonal mirrors, index 4 subgroup); all of these are isomorphic to [3]. the ringed coxeter diagrams are , , , and , representing different types (colors) of hexagonal tilings in the wythoff construction.