If you color rhombs with n colors at the four sides you get
(n^4+n^2)/2 one-sided and (n^4+3n^2)/4 two-sided
3 colors, 45 one-sided pieces:
3 colors, 27 two-sided pieces:
Turning the rhombs and choosing matching colors for the borders we get a hexagon. Instead of colors we can also
choose straight, male and femal borders.
4 colors, 136 one-sided pieces:
5 colors, 325 one-sided pieces:
The picture shows the method for the construction. Save all pieces with only green, teal, blue and yellow
edges for the second part of the construction. A few pieces with one wrong color as the two pieces with one red edge
are allowed, too.
5 colors, 175 two-sided pieces:
Since there are only five colors two couples of rhombs must get the same edge color.
6 colors, 666 one-sided pieces:
7 colors, 1225 one-sided pieces: