Neat. The multiple colors for groups is another innovation beyond SGT's Net.

You might consider implementing the traditional 3 mouse button controls (rotate left, mark correct, rotate right). If you can keep the Firefox context menu from popping up.

Maybe there's a way to support wrapping, and help the player understand which edge wraps to which? Maybe affecting the shape?

Related: 5 days ago "Simon Tatham's Portable Puzzle Collection (greenend.org.uk)": https://news.ycombinator.com/item?id=32170592