Rhombs with 3:1 Coloring

Why shoud we use sets of rhombs with exactly three sides same colored and one side colored with another color? If three colors are given we get 12 pieces with the above property, which can cover a single rhon with matching colors at the edges. Without this restriction we have too many rhombs and with only two colors the number of pieces is too small. Therefore I started to examine also sest of such pieces with more given colors. The sets are rather small due to the restriction and it wasn't that easy to get solutions for 7 colors or more.

3 Colors, 12 Pieces

Here are pictures of the 12 pieces and the covered rhon as physical object.

4 Colors, 24 Pieces

Two single rhons can be covered with this set.

5 Colors, 40 Pieces

The square of size 2 is a special tetrarhon with 40 faces. Some other tetrarhons are also connected at 4 faces and have a surface area of 4*12-4*2=40 faces.

6 Colors, 60 Pieces

A hexagonal ring of size 2 and a hexagon of equal size both have a surface area of 40 faces, because the center rhon of the hexagon hides 6 faces of the ring but contributes three additional faces each to the top and the bottom of the hexagon.