Received: from WAIKATO.S4CC.Symbolics.COM (TCP 20024231532) by AI.AI.MIT.EDU 28 Mar 88 16:50:43 EST Received: from ROCKY-MOUNTAINS.S4CC.Symbolics.COM by WAIKATO.S4CC.Symbolics.COM via CHAOS with CHAOS-MAIL id 165953; Mon 28-Mar-88 16:47:32 EST Date: Mon, 28 Mar 88 16:48 EST From: Allan C. Wechsler Subject: Magic Polyhedra and parity constraints To: Cube-Lovers@MIT-AI.ARPA Message-ID: <19880328214819.9.ACW@ROCKY-MOUNTAINS.S4CC.Symbolics.COM> In response to Peter Beck's thought-provoking idea about connecting Rubikoid puzzles to plate tectonics, I have two slight spoilers. First, plate tectonics involves spreading zones, which are places where new crust is created, and subduction zones, where crust is destroyed. In any permutation group, the things being permuted are not allowed to appear or disappear. So it seems unlikely that group theory can be directly applied to tectonics. Second, just because a puzzle is Rubikoid does not mean it has parity constraints. Consider the "Magic Octohedron", which has eight triangular faces. You can grab any pyramidal cluster of four faces and rotate it. This is really the 2x2x2 Cube in disguise. In this form, it has no parity constraints, that is, all the 8-factorial different configurations are achievable. So even if group theory could be applied to tectonics, we couldn't assume parity constraints in the general case.