Pretty Patterns

Order 1680

Permutation
(ulb,rub,dlf,luf,dfr,rbd,urf)
(ur1,rf1,ld2,fr2,lu1,lf2,rd1,rb2,fd2,df1,ru2,ub1,fu1,db2,bu2,dr2,fl1,uf2,bl2,ul2,br1) (bd1,lb1,dl1) (bd4,lu4,fd3,ru3) (dr3,uf3,dl4,ub4) (bu3,fu4,ul3,ur4,lb4,rf4) (rb3,fl4,lf3,br4) (bd3,dl3,lb3)
(r1,+b2,++f3,-r4,+r2,-b4,l1,++b3,++d3,++l3,f1,u1,-l4,b1) (u2,++d4) (f2,++f4,l2,+r3) (d2,++u4) (r5,-f8,++u7,+r6,-r8,u5,-b8,-u8,+b6,+u6,+f6,-l8) (f5,+d6,++r7,+l6,++d7) (l5,++f7,-d8,b5,++l7) (d5,++b7) (r9,-d12,++f11,-b12,b9,++b11,f9,+r10,++u11,+l10,++l11,+u10,-r12,-l12,d9,++d11) (u9,-f12,+f10,+b10,++r11,+d10,l9,-u12) (r13,l13,+d14,-d16,+r14,d13,-f16,b13,+b14,-b16,+f14,++r15,-u16,++l15,-l16,++u15) (u13,+u14,f13,++f15,++b15,-r16,++d15,+l14)

Latin Square

Algorithm Michael Z. R. Gottlieb 2008
F R' B' D2 · F' B2 · D2 L D' F R' F' U' F' R' B R U2
TF TR' TB' TD2 · TF' TB2 · TD2 TL TD' TF TR' TF' TU' TF' TR' TB TR TU2
T3B T3L T3U2 T3B2 T3L' T3B T3U T3L' T3U2 T3L' T3B' (47 btm, 47 ftm, 58 qtm)

Algorithm Walter Randelshofer 2014
U SF SR SU F2 SR2 B U SF2 D2 WR2 U WR2
TU S2F S2R S2U TF2 S2R2 TB TU S2F2 TD2 M2R2 TU M2R2
T3U2 T3B T3L2 T3U' T3L2 T3U T3B2 T3L' (34 btm, 48 ftm, 72 qtm)

Note
The color arrangement of each face builds a Latin Square. A Latin Square is an n x n table filled with n different symbols in such a way that each symbol occurs exactly once in each row and exactly once in each column.

© Walter Randelshofer. All rights reserved. TWIZZLE © js.cubing.net. All rights reserved.