Received: from ARDEC-AC4.ARPA (TCP 30003004020) by AI.AI.MIT.EDU 28 Mar 88 16:00:38 EST Date: Mon, 28 Mar 88 15:54:07 EST From: Peter Beck (LCWSL) To: cube-lovers@AI.AI.MIT.EDU Subject: magic polyhedra Message-ID: <8803281554.aa20390@ARDEC-AC4.ARDEC.ARPA> a puzzle fool's view of plate tectonics by peter beck april 1, 1988 what follows is an unfounded speculation of how "magig polyhedra" can be used to understand the manifistations of plate tectonics. my imagination was piqued while manipulating the "megaminx" (a dodecahedron with flat pentagon shaped faces, marketed in the usa by tomy) because the puzzle locks up when an attempt is made to turn too many faces simultaneously. this causes the surface to distort and when too much force is excerted the puzzle comes apart in an explosive fashion. i, impusively concluded that the geometric principles governing this explosion are analogous to what happens when the surface plates of the earth are rotated by the forces behind plate tectonics. this analogy is useful because it provides a macro model with physical parity constraints to study plate tectonics, eg, by helping forecasters tie together observable events around the world a better understanding of individual events could be obtained. another area of study could be the parity constraints on the motion of the plates, ie, the directions of plate rotation are constrained by their neighbors, because each plate does not move independently (see fig. 465.10 in fuller's book "synergetics"). [it should be noted that other dodecahedron magic polyhedra may be more appropriate for the study of plate tectonics; ie, the "impossiball" or 'alexander's star".] now that my fantasizing is in high gear i will expand my speculation to consider the engine that drives plate tectonics. i have decided that if one knew some physics it could probably be shown that a rotating sphere with a liquid center would develop 12 local circulations which the surface plates would float on. thus, plate tectonics can on a macro scale be reduced to a simple problem of fluid dynamics and some geometric parity constraints which can be displayed with magic polyhedra. the future is puzzling, but cubing is forever !! distribution: cff wgr cube-lovers@mit