If n colors are available the number of different one-sided pieces is (n^8+4n+2n^2+n^4)/8. For n>2 these numbers are rather high and I decided to look at subsets where only two colors out of n are used for each piece. It's also possible to include or exclude same colored pieces. If three or four colors out of n are allowed you can demand a fixed ratio of frequencies for these colors.
The picture above shows a construction choosing one or two colors out of three for the pieces. Typically pieces with many sides of same color are making kind of clusters.
The table shows the number of pieces for a lot of sets and subsets. Click the numbers to see some constructions.
|Colors||One or Two-sided||Number of Colors on Each Piece||Ratio of Color Frequencies|
|≥ 1||> 1||≤ 2||= 2||6:2||5:3||4:4||2:2:4||2:3:3||1:3:4||2:2:2:2||1:2:2:3|