From cube-lovers-errors@mc.lcs.mit.edu Mon Nov 10 11:32:49 1997 Return-Path: Received: from sun30.aic.nrl.navy.mil by mc.lcs.mit.edu (8.8.1/mc) with SMTP id LAA14072; Mon, 10 Nov 1997 11:32:48 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Mail-from: From cubeman@idirect.com Sun Nov 9 23:05:52 1997 Message-Id: <34668899.248A@idirect.com> Date: Sun, 09 Nov 1997 23:07:53 -0500 From: Mark Longridge To: cube lovers Cc: joyner.david@mathnt1.sma.usna.navy.mil Subject: Megaminx, the 10-spot and GAP First of all, the STANDARD colour arrangement used by Ideal Toy is as follows: UP = White DOWN = Blue FRONT = Yellow BACK = Green LEFT = Red RIGHT = Orange All the official Ideal Toy 2x2x2, 3x3x3 & 4x4x4 cubes used this arrangement. Even my 5x5x5 cube is the same. Secondly, I have at last resolved the 10-spot pattern for the megaminx in GAP. I created the process m1a which is the sequence of operators to generate the 10-spot. I had no C_U operator, so it was more difficult than I thought it would be. To see all the gory details surf to the following URLs (These are all GAP text files) http://web.idirect.com/~cubeman/dodeca.txt describes the megaminx http://web.idirect.com/~cubeman/megaop.txt describes operators http://web.idirect.com/~cubeman/spot.txt generates the 10-spot Note that after executing spot.txt (which loads the other necessary files) in gives the order of process m1a correctly as 5. This generator uses all of the megaminx operators except the top and bottom faces, so it is a pretty good test of the correctness of the all of dodeca.txt, megaop.txt, and spot.txt I believe this is the first simulation of the megaminx generating the 10-spot although Dr. David Joyner is very close! His work is more graphically interesting (using Maple to generate 3d pics of the megaminx) but his operators to rotate the whole megaminx are cooked. However, we have both verified that processes m2, m3 and m3a are correct and have been graphed correctly using Maple. -> Mark <-