From cube-lovers-errors@curry.epilogue.com Sun Mar 23 14:19:14 1997 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 OAA02111; Sun, 23 Mar 1997 14:19:14 -0500 Precedence: bulk Errors-To: cube-lovers-errors@curry.epilogue.com Message-Id: <199703231549.QAA15923@sun529.rz.ruhr-uni-bochum.de> Comments: Authenticated sender is From: bandecbv@rz.ruhr-uni-bochum.de To: cube-lovers@ai.mit.edu Date: Sun, 23 Mar 1997 17:47:14 +0000 MIME-Version: 1.0 Content-type: text/plain; charset=ISO-8859-1 Content-transfer-encoding: Quoted-printable Subject: Super-skewb Priority: normal X-mailer: Pegasus Mail for Windows (v2.42a) > Anybody have any good moves ... (Stan Isaacs, 19 Feb 1997) > Several people asked ... (Stan Isaacs, 20 Feb 1997) > Hi, Cube-Lovers! My name is Chistoph Bandelow, and I am new in this exclusive club. Having finally aquired a modem and the necessary software a few weeks ago, I'm still overwhelmed and confused by everything. I have read all the contributions from July 1996 till now and the complete "Index by Subject". To begin with something, I would like to make some remarks about the Skewb, especially the wonderful Skewb variations made by Tony Fisher. I suggest to call them "Fisher's Icosahedron", "Fisher's Dodecahedron", and so on..Owing all of these puzzles, I am very enthusiastic because of their originality and first-class quality. Just in case you are considering to acquire one or the other from him: Tony Fisher is a very reliable, modest and decent person. THE SKEWB has been first described to a larger public by Douglas R. Hofstadter in the July 1982 edition of Scientific American. This treatise is included in Hofstadter's book "Metamagical Themas" (Basic Books 1985 and Bantam Books 1986). It was here where Hofstadter suggested the name 'skewb' as a reminder of skew and cube. One of the wonderful features of the Skewb is that we don't have to quarrel how to count single moves: no trouble with outer layer moves versus slice moves or with 90=B0 moves versus 180=B0 moves, there is just one type of move rotating one half of the Skewb by 120=B0 against the other half. >From 1985 to 1988 I had an intensive correspondence with Ronald Fletterman where I used the following NOTATION: Hold the (ordinary cubical) Skewb such that there is a unique Right upper corner, Left upper corner, Front upper corner and Back upper corner. R, L, F and B respectively denote a clockwise 120=B0 rotation of the associated half cube (as seen from the outside). R', L', F' and B' denote counterclockwise turns. Small letters r, l and so on are used for rotations around the bottom corners. Though this notation is short and handy, it is probably not as good as the one used by D. J. Joyner in his Skewb page (see http://www.nadn.navy.mil/MathDept/wdj/rubik.html) But I stick on my old notation, especially after Ronald Fletterman, used this notation in two papers in CFF (Cubism For Fun, the newsletter of the Dutch Cubist Club) in which he provides an enormous collection of Skewb maneuvers, see CFF 17 (May 1988) and CFF 18 (September 1988). The square center pieces of the Skewb can only rotate pairwise and only by 180=B0, not by 90=B0. Ronald Fletterman's collection covers these "invisibles". He, the perfectionist, gives maneuvers for all 5 possible cases: 2 neighboring squares, 2 opposing squares, 4 squares all but 2 neighborings, 4 squares all but 2 opposing, all 6 squares. However, all his other maneuvers (those for the corner pieces of the Skewb) pay absolutely no heed to the orientation of the center pieces. Every short and elegant solution method for the new Skewb variations of Tony Fisher or for the beautiful round versions of the Skewb like Mickey's Challenge or Sonic's Puzzle Ball or the Mach Balls require maneuvers for the corner pieces which do not twist the center pieces. Some of those maneuvers are given in my 80 page booklet about Mickey's Challenge or about Sonic's Puzzle Ball or on the leaflets accompanying some other puzzle balls from Meffert. Here is a selection: SOME SUPER SKEWB MANEUVERS. 1. (FL'R)^6 (18) twists the 2 neighboring squares on the left side. 2. R'BLF'L'FRLB'R'FRF'L' (14) achieves the same thing. 3. FfRr'f'FfF'R'f'rRF'R' (14) twists the top and bottom square. 4. (RF')^2 (R'F)^2 (8) twists the four top corner pieces: ... the right and front one clockwise, the left and back one counter- ... clockwise, in short: (+R) (+F) (-L) (-B). 5. R'FR' (F'R)^2 fF'f (Ff')^2 (14) twists 2 corner pieces: (+R)(-L) 6. rF'rfR'F'rfR'r'F (11) twists the top front corner piece clockwise ... and exchanges (3-cycles) the 3 neighboring corner pieces, ... in short: (+F) (L,R,f). The very last notation does not precisely ... describe the effect of the maneuver since the orientation of the ... three corner pieces is not given. A remarkable and fundamental ... difference between Rubik's Cube and the Skewb is that the Skewb ... does not allow pure corner-3-cycles: It is impossible to achieve ... (L,R,f) without any other corner piece change! CALL TO CUBE-LOVERS: I'm convinced that the maneuvers given above, especially number 2, 3 and 5, may be improved. Who can give shorter maneuvers or a good maneuver for (+L) (+R) (+f) ? PROPAGANDA. One last remark: I don't want to offend the good rules of netiquette by doing any kind of advertising here. But to avoid unnecessary questions and loss of time, allow me to say that I will send my free mail order cube catalog (1996 edition, this is still the latest) to everybody who requests one and provides his postal address. Christoph Christoph Bandelow mailto:Christoph.Bandelow@rz.ruhr-uni-bochum.de