This is a graphical arrangement puzzle. Consider the following 36 tiles:
Each tile has up to 8 connected directions and each tile has an initial up side. (The edge to whose centre the central pentagram points is the upper edge.)
These tiles have to be arranged into an arbitrary, single polyomino with a single restriction:
No tile may be placed such that a (brown) connection points directly at another tile that isn't pointing back.
Note that it is possible to have a connection pointing at "nothing" (on the edge of the polyomino), but if it points at another tile, then that tile must have a connection pointing back.
The resulting polyomino is scored like this:
Dissect the polyomino (however you wish) into smaller rectangles such that each tile is part of exactly one such rectangle.
The number of inner edges in these rectangles - i.e. all edges which connect two tiles of the rectangle - are counted, and that number is squared.
If any tile was rotated from its original position, a value has to be subtracted from your score: This value is the square of the total number of 90° rotations used (compared to the original tile-set.) For example, if one tile was rotated clockwise by 90° and another by 180°, then the total number of 90° rotations is 3, and the penalty is $3^2=9$.
Bonus score: Solutions which include all 36 tiles in a square are ranked by the number of 'separate networks' they form - the less networks the better, i.e. the ultimate solution additionally forms a single "brown" network.
Find the highest possible score for this puzzle.
(The tile-arrangement has to be shown.)
Example of a valid arrangement (only 9 tiles):
As no tile was rotated, the score of this set is $7^2 + 1^2 + 0^2 = 50$ ( A 2x3 rectangle has 7 inner edges, a 2x1 rectangle has 1 inner edge, a single tile has no inner edge. )
Example of an invalid arrangement (only 9 tiles):
The bottom-right corner tile points towards the central tile, which isn't pointing back.
2nd Example of an invalid arrangement (only 4 tiles):
Both C4 and A4 point at a tile (the one diagonal below) which is not pointing backwards. (That they two 'link' with each other via the corner is not important.)