There are only three trihexes and all of them are symmetrical. They can form exactly 951 different shapes. Out of these shapes 896 have unique solutions; 37 have two solutions, 16 have three solutions and just 2 shapes have four solutions. These are the champion shapes for the trihexes. They are shown below are with all their solutions:
As it can easily be seen, both champions use the same pattern: there are three solutions derived from different orientations of the side 3 triangle formed by the Bar and Triangle trihexes. There is a fourth solution which breaks the triangle.
This result shows once more that shapes with multiple solutions comprise regions which can be rotated or mirored on their own, thus forming groups. Both champion shapes above use this principle. In addition, the last solution of Africa is related to the second solution by a mirroring of the region composed of the Triangle and Arch trihexes; the last solution of Asia is related to the first solution by a mirroring of the region composed of the Bar and Arch trihexes.
Having all the shapes that a set of polyforms can tile enables us to look for various properties. Out of the 951 shapes only six are symmetrical and all they have unique solutions:
Only ten shapes have a hole and only one of these has a hole of two hexes. This is the biggest trihex farm:
The minimal perimeter of a trihex shape is 22 and there is only one such shape:
Maximal perimeter is 36 and there are 248 shapes that correspond to this, too many to be interesting.