From cube-lovers-errors@curry.epilogue.com Sat Jul 13 04:22:06 1996 Return-Path: cube-lovers-errors@curry.epilogue.com Received: from curry.epilogue.com (localhost [127.0.0.1]) by curry.epilogue.com (8.6.12/8.6.12) with SMTP id EAA00266; Sat, 13 Jul 1996 04:22:06 -0400 Precedence: bulk Errors-To: cube-lovers-errors@curry.epilogue.com Message-Id: <31E75D1A.2754@durham.net> Date: Sat, 13 Jul 1996 01:23:54 -0700 From: Steve Huff Organization: Huff Corp X-Mailer: Mozilla 2.01 (Win16; U) Mime-Version: 1.0 To: cube-lovers@ai.mit.edu Subject: Megaminx Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Content-Disposition: inline; filename="MEGAMINX.TXT" Well I was on the right track long ago, but now I have confirmation. The megaminx has a slice group, analagous to the cube slice group. All the possible spot patterns are in the megaminx's slice group, e.g. the 10 spot and the 12 spot patterns. With process M1 we may easily generate any spot pattern, although there is much room for improvement. The slice group of the megaminx is generated by turning the faces opposite to each other in the same direction (i.e. same direction looking at a face head-on!) It is a small enough group to seach from head to tail, although the exact details are still being worked on. In the case of process M1, L is opposite to R, not just separated by a face F, as in processes M2 and M3. My original diagram is rather limited, but it does illustrate the idea of L & R separated by F only (as opposed to a real opposites but I have no satisfactory notation). /\ / \ / \ \ U / L \ / R \____/ F Moves for the Magic Dodecahedron (Megaminx) ------------------------------------------- C_U = Rotate entire dodecahedron clockwise via the U face suffix notation: f = face turns u = unit turns M1 10 spot (L1 R3 C_U)^36 (slice group) (72f) M2 3 cycle of edges (uf, lf, rf) R+ F+ U+ F- U- R- L- U- F- U+ F+ L+ (12f) M3 2 flip L-- R++ F+ U- R+ U+ L++ R++ U+ (18f, 26u) R-- L-- U- R- U+ F- R-- L++ U-