I did it!
After pondering and being frustrated by this puzzle for over a week and bugging my, (now fellow) potentate of the rose, to keep rolling and computing for me so that I could figure it out, she sent me to this website so that I'd leave her alone.

after about 2 hours and 100+ rolls, I discovered the secret.

I am now driving my Math Teacher crazy with the puzzle. (don't worry, I'll never tell) and so today I sent her this link, and so the cycle continues....