Hexagons

If you color squares with n colors at the four sides you get (n^6+n^3+2n^2+2n)/6 one-sided and (n^6+3n^4+4n^3+2n^2+2n)/12 two-sided distinct pieces.

3 colors, 92 two-sided pieces:

In the one-sided set there are 130 pieces with up to three colors. Jared McComb suggested to discard the three single-colored pieces and wanted to construct a regular hexagon with the remaining 127 pieces. Starting with the border positions I got this solution:

Jared also noticed, that the number of one-sided two-colored pieces without the single-color ones is 12 and suggested to tile the plane with irregluar hexagons composed of these pieces. Tessalation with those hexagons and parallelograms are shown below.

We can't get neither a hexagon nor a parallelogram with same colored border, because the number of pieces with two or more consecutive sides of this color is too small.

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