Date: 6 August 1982 19:51-EDT From: Allan C. Wechsler Subject: Invisible group of the 4^3 To: CUBE-LOVERS at MIT-AI The 4^3 doesn't have a supergroup in the sense of the 3^3 -- the orientations of the ceter cubies are determined by their positions. However, there is one fairly natural adjunct group that people might try thinking about and solving. A 4^3 shows 24 center cubies, 24 edge cubies, and eight corner cubies. But if it were really a solid cube chopped up by parallel slices, it would have eight more cubies buried inside. Call them stomach cubies. The eight stomach cubies form a 2^3 buried in the 4^3. They move when you twist slices. Can people come up with tools to frob the stomach cubies without disturbing the visible cubies? What is the order of the adjunct group? --- Allan