From cube-lovers-errors@mc.lcs.mit.edu Fri Jul 24 13:30:22 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil by mc.lcs.mit.edu (8.8.8/mc) with SMTP id NAA02692; Fri, 24 Jul 1998 13:30:20 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Mail-from: From cube-lovers-request@life.ai.mit.edu Thu Jul 23 18:21:31 1998 Date: Thu, 23 Jul 1998 18:21:02 -0400 From: michael reid Message-Id: <199807232221.SAA07643@hilbert.math.brown.edu> To: cube-lovers@ai.mit.edu Subject: patterns on 5x5x5 cube a while ago, rainer asked for patterns on the 5x5x5 cube. here are some i know (the hardest part seems to be finding the scraps of paper on which the maneuvers are written). standard notation uses R and r for 90 degree clockwise twists of the outer layer and second layer, respectively. i've found it convenient to have notation for Rr , so i use _R_ (that is, capital R underlined). i guess this notation is more convenient for handwritten maneuvers, but not so convenient for e-mail. i'll use _R_ to denote R underlined and _( F L U B ... )_ to mean that the whole thing inside the parentheses is underlined. the first pattern is a "double" snake; it meanders onto each face twice. _R'_ b' _U_ F2 _U'_ b _U_ F2 _(U' R2 F')_ u2 _(F U L')_ u2 _(L U' R' L)_ f _D'_ B2 _D_ f' _D'_ B2 _(D L2 B)_ d2 _(B' D' R)_ d2 _(R' D L)_ if i understand the terminology correctly, this is a continuous non-chiral isoglyph with the pattern ...*. **.** .*... .*... .*... i still remember that when i found this pattern some 10-12 years ago, i saw the URF faces together. then i turned the cube around, and was surprised by how it continued on the other three faces. (i shouldn't have been surprised, but you know how that goes ... ) i came across this pattern accidently. then i went snake hunting, and found several others: snake 2 _(R F2 R2 U2)_ r2 _(U2 R2 F2 R' D' F2 B2 D R F2 R2 U2)_ r2 _(U2 R2 F2 R' D')_ r2 _(F2 B2)_ L2 _(R2 U' D F2 B2 U)_ those two have the property that the two snake segments on each face have the same color. if this condition is relaxed, we also have snake 3 _(R L' F U2 R F2 R2 U2)_ r2 _(D2 L2 F B' D' F B' U' D F R L D' B2 L' F B' D')_ f2 _(U2 D2)_ f2 _(U' D2)_ this one can be modified slightly; change the U and D faces .*.*. .*.*. .*.*. .***. .*.*. ..... from .*.*. to .***. .*.*. .*.*. if only one is changed, then we get two separate snakes. there's also snake 4 _(D F2 B2)_ l2 _(F2 B2 R')_ R2 _(F2 R2 U2)_ r2 _(U2 R2 F2 R' D' F2 B2 D R F2 R2 U2)_ r2 _(U' D' F' U2 D2 B U' D L2 B2 L' U2 D F2 B2)_ another interesting pattern is U R' U' F' _U'_ R' _U_ f _U'_ R _(U F')_ F2 U R U' _B_ l' _D2_ l _D_ f' _D2_ f _(D' B')_ D' L D B _D_ L _D'_ b' _D_ L' _(D' B)_ B2 D' L' D _F'_ r _U2_ r' _U'_ b _U2_ b' _(U F)_ which gives a continuous non-chiral isoglyph with the pattern .*... .*... .*... ***** ...*. the same maneuver produces an analogous pattern on the 4x4x4 cube, but there's probably an easier maneuver. another isoglyph (also continuous and non-chiral) with the same pattern is R f' U2 f U l' U2 l U' R' _D'_ L b2 L' _B'_ U b2 U' _(B D)_ L' b D2 b' D' r D2 r' D L _U_ R' f2 R _F_ D' f2 D _(F' U')_ modifying this pattern is how i found the first double snake. mike