I've trying to work on an algorithmic solver for dodecahellspawn, instead of the current roll-back-the-moves method, and boy has it been a mess. I think my group theory lessons were much too long ago for this.

Unlike the Honeycomb puzzle, the moves on the dodecahellspawn forms a non-abelian group, which makes things an order of magnitude more complicated. At least I've managed to convince myself that the texturing doesn't really affect the complexity of the solution at all. Ironically enough, it might actually make things easier.