This set with 51 pieces is rather large and I decided to write a program to solve the problems. At first I tried to construct the two possible jagged rectangles. The little dots in the center show the color on the back.

Then I wanted to make three congruent figures with strict coloring on the front and uniform coloring on the back to complete my mobile with tetrahexes.

I didn't have much success until I split the whole set into three subsets each of which can be derived from the others by a cyclic shift of colors. With a solution found for one subset the other parts are given, too. For one jagged rectangle a third of the solution is shown. For the other rectangle look at the mobile. Hexagon shapes with holes can also be solved.

At last the splitting of the whole set can be used to make some rings with connected coloring on the back.

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