I liked the concept but I have a few suggestions.
1)I scoring system would be nice
2)My find on the limited solution set
I read the instructions briefly and believe that the idea is to solve the puzzle in N moves whereby N is equal to the level. If I am correct on this notion, I found your game more challenging; at least thought provoking on levels where N<12 or so. After that I found I was able to solve the puzzle with N rotations (again N being == to the level #) by a simple pattern without any actual thought.
for instance...
I choose one pentagon (for instance say the bottom right)
and I go around to the other 4 looking for a match. If, it doesn't work I rotate the staring one and then again rotate the other 4 until
I have a solution. I haven't bothered solving the permutations and combinations, but just by observation most levels were solved in under 10 rotations. Perhaps I was in a consistantly lucky state.
In other words, It is too simple to solve the puzzle with no thought that I found it hard to even try actually thinking about solving each level in the least amount of moves possible.
3)perhaps a countdown timer is in order. In which when it reaches 0 the pentago's automatically randomize.
4)Perhaps try different level layouts. Or add other surprises for instance you could have the colors on certain pentago's rotate every so often. (I don't mean that the actual pentago rotates but just's it's colors cycle), this would mean that the player may have to wait for a certain color cycle rotation to have a solvable puzzle.
5)I haven't tried working out other strategies of play but I'm sure with some imagination you can offer multiple level solutions. For instance perhaps the outer arms can be alligned to border colors for a variation on connecting the inner arms. ect Introduce a something like an upgrade where the player has a small amount of time to rotate only one pentago without affecting others.
6)Change up the rotation scheme. In other words possibly turning one pentago causes the pentago diagonally accross to rotate instead of just the one next to it
These are just a couple ideas. Hope they help.
Btw, I did enjoy the game. And with some more effects, and strategic level building, this very well could prove to be a very addictive puzzle game. Keep working on it!
~zen