Three Sets Of Colored Trihexes
Since all three trihexes are symmetric there is no difference between the two-sided and the one-sided set.
We have 3*3=9 pieces with a total of 27 hexagons. A triangle of size 7 consists of 28 hexagons, too large for the set. But we can remove one hexagon and we get a pattern which can be solved by the set. Only for one position of the removed hexagon a solution is impossible. If the hexagon is removed from one corner we gwt a trapezium which is shown below.
A hexagon with symmetry under 120 degree rotation is also possible,
Beside triangle symmetry we have also constructions with two axes of symmetry, one axis of symmetry and almost convex pentagonal shapes.