Pretty Patterns

This is the largest collection of pretty patterns that is known to me. It has been compiled by Mirek Goljan, who is also the author of most of the moves. Significant contributions were made by Peter Nanasy, Michael Reid, Mark Longridge, Hans Kloosterman, and others.


Notation and terminology
Regular patterns
Letters on all faces
U's ornaments
U's semi-ornaments
Supplements of the U's (Czech check problem)
T's simple patterns
J's ornaments
Supplements of the J's
I's semi-ornaments
Supplements of the K's
6 L's from Q2
6 L's from Q1
Regular ornaments
Regular ornaments -supplements
Semi-regular patterns
Semi-regular ornaments
Semi-regular ornaments - supplements
Ornaments composed from U2, U3 or U4
Semi-regular semi-ornaments
Even positions
Odd positions
Cyclic patterns
Three-color regular patterns
Three-color regular ornaments
More-color regular patterns
More-color nonregular patterns
Flips and twists
Patterns possible by disassembly
Regular semi-ornaments
Semi-regular semi-ornaments
Cyclic patterns
Simple patterns
One little square of opposite color
Two little corner squares of opposite color
Odd simple patterns


The usual notation U, R, D, L, B, F is extended to slice and antislice moves.
Us,Rs,Ds,Ls,Bs,Fs are slice moves UD',RL',DU',LR',BF',FB'.
Ua,Ra,Da,La,Ba,Fa are antislice moves UD,RL,DU,LR,BF,FB.
Sr, Sl, Sf, Sb, Su, Sd are the center slice moves adjoining faces R,L,F,B, U,D.
[P*Q] means the same as P Q P'
[P;Q] means the same as P Q P'Q'
Lowercase letters u,r,d,l,b,f represent twists of the whole Cube, so that u = UsSu, r = RsSr and so on. For example dFR'U = LF'Ud = LF'U.
Character ^ represents mirroring (usually R<->L).

Here is Mirek's classification of two-color patterns which he introduced in 1982.

1. Ornaments
A typical example of an ornament is "cube in cube". Colors of the faces are mixed: (U->R->F)(D->L->B). Axis of each pattern goes through the corners URF and DLB. In order to desribe ornaments in a short, symbolic, form the following notation is introduced:
D is an exchange of the centers (F,U,R) (L,D,B)
V are twists of the corners FUR+ and LDB-
S is a permutation of the edges (FU,UR,RF)
S' is a permutation of the edges (LB,BD,DL)
L is permutations of the edges (FU,FR,UR) (LB,LD,BD)
O is a permutation of the corners (FUL,URB,RFD)
O' is a permutation of the corners (LBU,BDR,DLF)
H is a permutation of the edges (UL,RB,FD)
H' is a permutation of the edges (UB,RD,FL)

2. Semi-ornaments
Every face has at most two colors which are mixed: (F<->R)(B<->L)(U<->D)
D is an exchange of the centers (FR)(BL)(UD)
W are flips of the edges FR and BL.
O is an exchange of the edges FL and RB.
R is an exchange of the corners FRU and RFD
R' is an exchange of the corners BLU and LBD
K is an exchange of the corners FLU and RBD
K' is an exchange of the corners FLD and RBU
S are permutations of the edges FU, FD, RU, RD
S' are permutations of the edges BU, BD, LU, LD
D is used to shorten the notation. [D] = [WORR'KK'S(14)(23)S'(14)(23)]
The alphabetical order of letters is: D,W,O,R,K,S.
Patterns containing all of R, R', K, K', S, S' are mostly denoted as [D...]. You should use mirroring (F<->R) to get K rather then K' and S(1.. rather then S(3.. or S(2.. .

3. Cyclic patterns
Every face has at most two colors which are mixed: (F->R->B->L)(U<->D)

4. Simple patterns
Every face is a simple two-color combination of colors from opposite faces of the Cube: (U<->D)(R<->L)(B<->F)

5. Specials
Other permutations of colors, for ex. (F->L->U->B->R->D) or (F->B->L->R) (U<->D)


Regular patterns are patterns which have all faces of the same look except for coloring and mirroring.


F U L'B°L F²D'F D F L'D'L F L'D B°L U'F' 21,20 [OKS(14)S'(23)] 2 peaks
° can be replaced by the same but otherwise arbitrary exponent
U F'D'L B²L'D F D L²U'aF²D'F²L² 21,16 p117 Improve RCC 3.9.36 (K)
D U²F²D²sR²sB²R²sD 20,11,8 [RR'KK'] crosses
D R²sDaRaF²sRaU 16,12,10
D RsFaL²F'aLsD'aL²U 16,14,12
U'R'F'U'R²sD B R'L²D²B²D²sB²U' 22,16,14 [ORR'KK'S'(12)] p147 ML's 6 ARM Pattern (K)
R U'F R'B'D²R'U'BsLsD B L U'R'U'F U'Ls 23,22,19 [DK] MG.1982
RaB'D'aL'R²D²F²R F'aU'F²R²U D²L² 25,18 p68 Cherries (K)
D'F²DsB²RsU RsB'R²B LsU RaB²U 24,20,16 [DOS(23)S'(14)]
(R²D L²)^4 Ds 22,14,10 [RR'KK'S(1342)S'(13)] p163 4 ARM Full

Letters on all faces

The U's - ornaments

BsU F'LsD F'U'BsR 12,12,9 U1 = [DH] P.Nánásy
F'R²D'RsF RaF D B LsU'F' 16,15,13 U2 = [DL] E.V.Chacøn
U B U'LsDsBsD R'UsB U'B' 16,16,12 U3 MG.1983
B R D'R FsD'RsF UsL'F U'L' 16,16,13 MG.1982
L D BsR'F L'F'DsR F R'D' 14,14,12 U4 MG.1982
R B'LsD U²BsR'L²DsF D' 16,14,11
R B²F UsL'FsU RsB'F²D' 16,14,11
L'F'aR'DsB R F LsD'L D 14,14,12 U5 MG.1982

The U's - semi-ornaments

R'aB²RaD'aL BsD'B²D FsL'D² 20,17,15 U6 [0+0] MG.1982
B LsD'LsB²RsD'LsF'aD²sFDs 22,19,13
U'LsF'UsL²B²L'BsD B² 16,13,10 U7 [4+0] MG.1983
F'L'FsR'F'D'F R BsL B L²BsD' 18,17,14 MG.1982
B F²D²BsR'BsL'F DsR'F RsB'R 20,18,14 U8 [2+2] MG.1982
R'F²LsD²B RsF L UsB'L'BsR'B 20,18,14 U9 [3+1] MG.1982
L'B'LsF'L'UsB L FsR F U²FsR² 20,18,14 U10 [1+3]

Supplements of the 'U's

Here are some positions with exactly 8 squares correct on every face. The remaining positions are discussed in the article "A Czech Check Problem" by Michael Reid, Cubism For Fun 36, Feb 1995.

LsF L'FsU F'U'BsR 12,12,9 DU1 = [H]
R D'LsF'RsD LsF L' 12,12,9
F'R²D'RsF RaF D F UsL'U' 16,15,13 DU2 = [L] MG.1982
F L F'RsD R'UsB U'B' 12,12,10 DU3 /E5/ MG.1983
U L B'D BsR'FsD BsR'F L'U'=(ULB'DBsR'FL'U')² 16,16,13 MG.1982
L U B'D BsR'FsD BsR'F U'L'=(LUB'DBsR'FU'L')² 16,16,13 MG.1982
U L'DsF'UsL DsF D' 14,14,12 DU4 MG.1983
UaL'DsF'UsL DsF D² 14,13,10 DU5
D'R'aD'RsF R F LsD'L D 14,14,12 MG.1982

The T's - simple patterns

R²U²R²U²R²FsU²Fs 16,10,8 T-ordinary MG.1982
L²D²R²D²L²FsU²Fs 16,10,8 MG.1982
L²D²B²D²F²L²B²U²B²U² 20,10 p97 6 T's A
FaU²FaR²D²R²U²R²B² 18,11,10 T-orthogonal MG.1982
F²D²R²U²B²D²B²R²B²D² 20,10

The H's

R²BsR²sBsL² 12,8,5 H1. - simple pattern
L²(U²F²s)²L²F²s 20,10,7 p174 6 H order 2 type 1
FaR²F²sD²sL²F'a 16,10,8 H2. - simple pattern
RaDaRaD²sRaDaRa 16,14,13
R²B²U²R²L²U²F²R² 16,8 p175 6 H order 2 type 2
R'aUaR²sF²sUaRa 16,12,10 p175a
R²F²sR²D F²sU²R²sD 20,11,8 H3. - semi-ornaments
U²R²sD F²sR²F²sR²U 20,11,8
R²sU'F²sL²F²sL²D 18,10,7 H4. - cyclic pattern
D'L²F²sL²F²sD R²sDs 20,12,8
R²sD'FsR²BsRsB²RsU 18,14,9 H5. - specials
D²R²F²U'F²sD R²sF²L²D² 22,12,10

The J's - ornaments

F'R²D'RsF RsF D'R²D F'L²F D'R²D²B LsU'F' 28,23,20 DLV MG.1982
U'R B'R'U R'D²F U F U'F'D'U²BsLsD F 22,20,18 U4V MG.1997
R'U'B L'B'L²U R U'L'U L D BsLsU'L F'L²F 24,23,21 U4V MG.1997
R²F'D'F²L F'R F R'aF'D B LsDsF'U² 22,19,17 U5V MG.1997
R²F'D'F²L F'L DsBsL D'aR'B R B'U² 22,19,17 U5V MG.1997
R'B'L²U'F'U L'B R²B'L'B R DsBsL Da 22,20,18 U5V MG.1997
R²F'D'R'D F L'F'aR F R'B RaU'BsL Da 22,21,20 U5V MG.1997

Supplements of the 'J's

R²U²B'U R B DaR B R'B'D'aR'B'U F²D'F²R² 26,21 LV MG.1997
U'R B'R'U R'D²F U F U'F'D²U'R U 18,16 DU4V MG.1997
R²F'D'F²L F'R F R'aF'D F D'R² 18,15 DU5V MG.1997

The I's - semi-ornaments

U²R²D²U²R²D'a 12,7

The K's

There are 5 "K"-ornaments that can be obtained as a composition of "U"- ornaments and crosses-ornaments. Another 5 "K"-semi-ornaments can be obtained as a composition of "U"-semi-ornaments and crosses-semi-ornaments, and 2 "K"- simple patterns can be obtained from the one-edge-little-square simple patterns


composed with a chessboard simple pattern.

Supplements of the 'K's

D'L'DsF R D'LsB L'R²B'UsR²DsB'R²D²R UsLsD'F' 32,28,22 [DLHH']

The L's - simple patterns

The first 14 types are members of the square group Q2. I tried to get algorithms minimal in q-moves and using a square group method too. Next 10 types are members of the group Q1. Q1 contains simple patterns which are not achieveable by square moves. For example

U'F R F²R'F'U²R'F'R²F R U' 16,13
U'F R F²R'F'U²F R F²R'F'U' 16,13
U'R F'R'F R F'R'F R F'R'F U 14

Q0 is the group generated by [F²,R²,B²,L²,U²,D²,(FUL,FDR)(FL,FR)].
Q0 consists of all positions whose colors of faces are two-color combinations of opposite faces of the Cube: (FB)(RL)(UD).
Q2 is the group of positions generated by [F²,R²,B²,L²,U²,D²], It includes the three-cycle of edges R²U²L²B²R²U²L²F² , E2+2 L²F²L²D²F²L²F²D².
Q1 is a group of positions generated by [F²,R²,B²,L²,U²,D²,(FUL,BUR,FDR)] - Q2,
Q3 = Q0 - Q1 - Q2 are odd positions. For example

D'F²U L²U'F²D'R²U F²U'R²D 19,13 This pattern is not pretty one, of course

6 L's from Q2

There are four groups of relative 6L patterns (14=1+1+4+8). A short bridges of the type X²Y² exist between the members of the group.

The first of them has the most interesting symmetries.

UsBsR²FaD'aF'aD²Fa 16,14,12 L1 MG.1982
F²L²B²U²L²D²L²U²B²U²B²R² 24,12 p176 6 L
FaL²F'aR²UsBsR²F'aUs 18,15,12 L2
L²D²B²D²B²L²B²L²B²D²R²U² 24,12 MG.1997
F'aD²BsLsD²Ra 12,10,8 L3 MG.1982
R²D²R²F²R²F²R²F²D²F²R²s 24,12 MG.1997
F²sL²D²L²B²L²F²L²F²D²B² 24,12 MG.1997
F'aUaL²DsBsR² 12,10,8 L4 MG.1982
R²D²R²F²R²F²R²F²D²F² 20,10 MG.1997
R²U²L²B²L²B²L²B²U²F² 20,10 MG.1997
FaD²BsLsU²R'a 12,10,8 L5 MG.1982
R²D²R²F²R²F²R²F²D²B² 20,10 MG.1997
R²U²L²B²L²B²L²B²U²B² 20,10 MG.1997
FaUaR²DsBsL² 12,10,8 L6 MG.1982
F²sL²D²L²B²L²F²L²F²D²F² 24,12 MG.1997
R²D²R²F²R²F²R²F²D²B²R²s 24,12 MG.1997

{L3} + R²s = {L4}, {L3} + F²s = {L6}
{L4} + F²s = {L5}, {L4} + R²s = {L3}
{L5} + R²s = {L6}, {L5} + F²s = {L4}
{L6} + F²s = {L3}, {L6} + R²s = {L5}

FaD²L²Fa 8,6 L7 MG.1982
U²B²R²B²U²B²D²F² 16,8 MG.1997
D²F²L²B²U²B²U²B² 16,8 MG.1997
FaD²L²FaD²R² 12,8 L8 MG.1997
U²B²R²B²U²B²D²F²D²R² 20,10 MG.1997
B²L²U²L²BsD²Fa 14,9,8 L9 MG.1997
D²F²R²D²F²D²F²D²F²D² 20,10 MG.1997
FaD²L²FaU²L² 12,8 L10 MG.1997
U²B²R²B²U²B²D²F²U²L² 20,10 MG.1997
D²F²R²D²F²D²F²D²F²R² 20,10 MG.1997
DsR²sDsF'aU²R²Fa 16,12,9 L11 MG.1997
U²B²D²sR²F²D²F²D²F² 20,10,9 MG.1997
DsL²UsFsR²F'aD² = L²UsB²RaF²R'aD'a 14,11,8 L12 MG.1997
U²B²D²sR²F²D²F²D²F²D²R² 24,12,9 MG.1997
U²B²R²B²U²B²D²F²D²R²U²s 24,12,9 MG.1997
LsU²sLsF'aU²R²Fa = BsD²RsF²U²F²R'aFa 16,12,9 L13 MG.1997
B²L²B²L²B²D²R²sF²R² 20,10,9 MG.1997
DsR²UsBsR²F'aU² = R²UsF²RaF²R'aDa 14,11,8 L14 MG.1997
= FaR²F'aR²UsF²Ua = FaR²F'aUaR²UsF² 14,11,10 MG.1997
D²F²R²D²F²D²F²D²F²R²U²s 24,12,9 MG.1997

  {L7} +D²R²={L8}, {L7} +U²L²={L10}
  {L8} +R²D²={L7}, {L8} +L²U²={L9}, {L8} +U²D²={L12}, {L8} +F²B²={L8}^
  {L9} +D²R²={L10},{L9} +U²L²={L8}
  {L10}+R²D²={L9}, {L10}+L²U²={L7}, {L10}+U²D²={L14}, {L10}+F²B²={L10}^
  {L12}+R²D²={L11},{L12}+L²U²={L13},{L12}+U²D²={L8},  {L12}+F²B²={L12}^
  {L14}+R²D²={L13},{L14}+L²U²={L11},{L14}+U²D²={L10}, {L14}+F²B²={L14}^

In this group ^ means F<->B symmetry.

A schema of short bridges:

Connections between L3, L4, L5 and L6 are of the type F²B².
Connections between L7,L8,L9,L10,L11,L12 and L13 are of the type F²R² and F²B².

            R²s                               /    \
        L3  ---  L4                      = L8 - L9 -L10 =
   F²s   |        |  F²s            U²D²    |        |   U²D²
        L6  ---  L5                      =L12 -L11 -L14 =
            R²s                              \     /

  = ... F²B² bridge to its own mirroring

Now let us consider bridges of the type F²R²sB². In this way, we get connections between L1, L2.

  {L1} + U²R²sD² = {L2}
  {L1} + F²U²sB² = ru{L2}
  {L1} + R²F²sL² = dl{L2}
  {L1} + D²R²sU² = {L2}
  {L1} + B²U²sF² = ru{L2}
  {L1} + L²F²sR² = dl{L2},

        /  |  \
      L2  L2  L2
       | \ | \ | \
      L2^ L2^ L2^
         \ | /

  ° ... center of the cube symmetry (FB)(RL)(UD)

We also get new connections between L3,L4,L5,L6.

  {L3} + D²R²sU² = {L5}^  (F<->B mirroring)
  {L4} + D²R²sU² = {L6}^  (F<->B mirroring)
  {L5} + D²R²sU² = {L3}^  (F<->B mirroring)
  {L6} + D²R²sU² = {L4}^  (F<->B mirroring)
  {L3} + F²R²sB² = {L6}^  (R<->L mirroring)        L3   L4
  {L4} + F²R²sB² = {L5}^  (R<->L mirroring)         | X  |
  {L5} + F²R²sB² = {L4}^  (R<->L mirroring)        L6   L5
  {L6} + F²R²sB² = {L3}^  (R<->L mirroring)

  {L7} + L²F²sR²  = {L9}^  (F<->B mirroring)
  {L11}+ L²F²sR²  = {L13}^ (F<->B mirroring)
  {L7} + F²U²sB²  = rr {L9}         {L9} + F²U²sB²      = rr {L7}
  {L8} + F²U²sB²  = rr {L8}         {L10}+ F²U²sB²      = rr {L10}
  {L11}+ F²U²sB²  = rr {L13}        {L13}+ F²U²sB²      = rr {L11}
  {L12}+ F²U²sB²  = rr {L12}        {L14}+ F²U²sB²      = rr {L14}

  About inversions:
  {L1}' = {L1}^   any mirroring along axis FRU--BLD
  {L2}' = {L2}^ (B<->U)(F<->D)
  {L4}' = {L4}^ (F<->R)(B<->L)               {L3}'   is not 6 L's
  {L5}' = f²u{L5}                            {L6}'   is not 6 L's
  {L7}' = {L7}^ (R<->U)(L<->D)               {L8}'   is not 6 L's
  {L9}' = {L9}^ (R<->D)(L<->U)               {L10}'  is not 6 L's
  {L11}' = {L13}^ (F<->B)(R->U->L->D)        {L12}'  is not 6 L's
  {L13}' = {L11}^ (F<->B)(R->D->L->U)        {L14}'  is not 6 L's
U R²U R²D²F²D R²F²U²F²U²F²D' 24,14 L'9 MG.1997
U R²U'B²D²L²U'F²U'F²D²B²D²F² 24,14 MG.1997
D²F²L²U²D B R B²R'B'D²R'B'R²B R D 24,17 L'10 MG.1997

  {L'4} = {L'3} + RsF²LsD²   f²d{L'4}  = {L'4}  + UsB²DsL²
  {L'5} = {L'3} + UsB²DsL²   f²d{L'5}  = {L'4}  + BsU²FsR²
  {L'6} = {L'3} + BsU²FsR²   f²d{L'6}  = {L'5}  + BsU²FsR²
  {L'9} = {L'8} + LsD²RsF²   f²d{L'9}  = {L'10} + RU²sL²U²sR
  {L'10} = {L'8}+ FsL²BsD²   f²d{L'10} = {L'10} + DsL²UsB²
  f²d{L'10} = {L'6}+ R²F²R²F²R²F²

  About inversions:

  {L'1}' = {L'1}^   any mirroring along axis FRU--BLD
  {L'2}' = {L'2}^  (F<->R)(B<->L)
  {L'3}' = {L'3}^  (F<->R)(B<->L)
  {L'4}' = {L'6}^  (F<->R)(B<->L)
  {L'5}' = {L'5}^  (F<->R)(B<->L)
  {L'6}' = {L'4}^  (F<->R)(B<->L)
  {L'7}' = {L'7}^  (F<->R)(B<->L)
  {L'8}' = {L'9}^  (U<->D)
  {L'9}' = {L'8}^  (U<->D)
  {L'10}'= {L'10}^ (F<->R)(B<->L)
There are two cases for the 6L's with respect to the corners:

a) the two opposite corners are in place (L1,L2,L7,L9,L11,L13), (L'1,L'2,L'7).
b) the two adjoining corners are in place (L3,L4,L5,L6,L8,L10,L12,L14),

Only two types have the same orientation for all L's (L1,L6).

Regular ornaments

F D R D'L'D R'D'F'R'F L F'R 14 [V]
L'D R'D'L D F L F'R F L'F'D' 14 [V]
R'D²R B'U²B R'D²R B'U²B 16,12 [V]
LsF L'FsU F'U'BsR 12,12,9 [H]
R D'LsF'RsD LsF L' 12,12,9 [H]
L'DsB D B'UsR D'Ls 12,12,9 [H]
LsF²R²D'FsU'F²sDFsDR²F²Rs 24,18,13 [SS'] MG.1982
R²F LsF RsU'F'U'F'RsU LsU R² 20,18,14 [HH'] MG.1983
R'B L B D'B D FsL'B²F U F'U'F'R 18,17,16 [HH'] Nánásy.1983
U'L'F L'F'R'F LsF'L F R F'R U 16,16,15 [OO'] MG.1982
U'R F'R'F L F'RsF R'F'L F L'U 16,16,15 [OO'] Nánásy.1982
U L D R²U R U'R B'D B'D'B²D'L'U' 18,16 [VH] MG.1997
R U'R B'D B'D'B L B'U R'U R U²B²R²L'U 22,19 [VSS'] 2 peaks MG.+JF.
R U'R B'D B'D'B L²U²F U F'U L'B R²L'U 22,19 [VSS'] 2 peaks MG.+JF.
? [VHH']
L²R'F D²L'F'RsFsL F U²L'B F² 20,16,14 [VOO'] crosses MG.1997
= C.ful.C', C = L²R'F D²L'F'Rs derived from p1
R'F²sR²U²sL'BsL'F²sL²U²sR'Fs 28,18,12 [VOO'] MG.1983
R'F²sR²U²sL'BsR'F²sR²U²sL'Fs 28,18,12 [VOO']
B'L F'L F R'F'L F R B'R'B R F'LsB'R B²L F L' 24,23,22 [VOO'] MG.1982
F R²sFaR²sF L B²sRaB²sL U²s 28,18,13 [VOO'] p101 (Plummer's Cross) (K)
? [SS'H]
U'F²U R U²R²U²R'F'R²F U'F²U 20,14 [HOO'] MG.1982
B'L'D L'D'L'F LsF'L F R F'L B 16,16,15 [HOO'] MG.1982
D L'B R D'R'D B'L B R'B'R D' 14 [HOO'] p87 Twisted Cube Edges

Regular ornaments - supplements

R'D²R B'U²B R'D²L DsBsR'F²L 20,16,14 [DV] MG.1982
U L F R'DsBsR'D R'D'F'R'F L F'R 18,18,16 [DV] MG.1982
BsU F'LsD F'U'BsR 12,12,9 [DH]
B R B'R²U'F'L U R D L U'B'L U L² 18,16 [DSS'] p86 Twisted Rings
LsF²R²D'FsU'F²sD LsDsB²F'U²R²Us 28,21,15 [DSS']
B'R'U'LsF R U²F R BsU'F'L' 16,15,13 [DHH'] snake R. Schoof
= C.u.C'^, C = B'R'U'LsF R U
U B²L D FsL'DsRsF'D²R' 16,14,11 [DHH'] p121 Improve RCC 3.9.31
U'R F'R'F L F'DsBsL U'R'D R D'F 18,18,16 [DOO'] Nánásy
U'R'DsBsL D'R'U'R DsR'D R U R'U F 20,20,17 [DOO'] MG.1982
U L D R²U R U'L DsBsR'B L'B'L²B'D'F' 22,20,18 [DVH] MG.1997
L F L D'B D L²F²D'F'R U'R'F²D 18,15 [DVSS'] (cube in cube)
= C.rf.C^, C = L F L D'B D L²F'
U²F²R²U'L²D B R'B R'B R'D'L²U' 20,15 [DVSS'] p7a (K)
F U²F'R'F²R²F'R U L D F'D'R²L'U'F U²F' 24,19 [DVSS'] MG.1982
F R B'L B R DsL'F'L UsB'R B R'U'R'U R'F' 22,22,20 [DVSS'] MG.1982
U F D'F²D F'R'F²R U'aB'U B²U'B L B²L'D 24,20 [DVSS']
U F'U²B U B'U²F U'LsB D'B²U B'U'B²D L' 24,20,19 [DVHH']
L²R'F D²L'F'DsBsD R F²D'L R² 20,16,14 [DVOO'] p1 6 X of order 3
= C.urb.C', C = L²R'F D²L'F'Ds
R'F²sR²U²sR'DsBsU'R²sU²F²sD'Ls 30,20,13 [DVOO'] chessboard
FsR²sU B²sU²R²sU L'U²sR²B²sL'Bs 32,20,13 [DVOO']p1a
RsF'DsB'D²sF DsBaDsF D²sB'DsB'Ls 28,24,16 [DVOO'] MG.1982
? [DSS'H]
B'L'D L'U'BsLsU'R DsR'D R U R'D L 20,20,17 [DHOO'] MG.
LsDsBsLs = DsBsLsDs = BsLsDsBs 8,8,4 [D]
R'DsBsLsD = U'BsLsDsB = F'LsDsBsL 8,8,5 [D]
L DsBsLsU'= D BsLsDsF'= B LsDsBsR' 8,8,5 [D]


F RsU²F²sU'aFsL'U R²sU²F²sD 26,18,13 chessboard of order 6 (K)
p2 6 X of order 6


Semi-regular ornaments

R'F'L BsD'F'D FsL'F²R 14,13,11 [S] (easy)
R U²L'UsB U'B'DsL U'R' 14,13,11 [S]
U F'U'F U RaU F U'F'R'aU' 14 [S]
R F²B'D'S'fD²SfD'B F²R' 16,13,11 [S]
R U F'U²sB U'B'U²sF R' 16,12,10 [S] p196
D R B'L²B R'B'L²B D' 12,10 [O] (easy)
D'L B²L'F'L B²L'F D 12,10 [O]
R'U F²D'F'D F²U'F R 12,10 [SO] (easy)
R'F²L'D'L F'L'D L F'R 12,11 [SO]
R'F'L F'D'F'D F L'F²R 12,11 [SO]
R'F'L BsD'F'D B'L'B L F L'B'F²R 18,17,16 [SO'] MG.1982
D L U'F'L'B'U B L F R²B'R'B R'aD' 18,17 [SO'] MG.1997
U R'F²R F D'F²D F'U' 12,10 [HO] (easy)
U F R'F R F D'F'D F²U' 12,11 [HO]
U'L²D B'D'L D B D'L U 12,11 [HO]
FsU'RsU'R²sD RsU Bs 16,14,9 [SH] MG.1982
B²R U²B²L'B'L B'U R'U B² 16,12 [VS] JF.1982
B²R U'R B'R'B²U'B'U R'U B² 16,13 [VS]
B²F'U F U'R U'B U'B'U R'U B² 16,14 [VS]
B²F'U F U'R U'R'U R'F R F'B² 16,14 [VS]
B'L F'L²FsR'B R F'LsB'R B²L F L' 20,18,16 [VO] MG.1982
F D R D'L'B'U'B D B'U B R'D'F'R'F L F'R 20 [VO]
LsU FsD F²sU'FsU'F L'FsU F'U'BsR 24,22,16 [SHH'] MG.1982
R U F'U²B U'FsD F'U²F D'R' 16,14,13 [SOO'] Nánásy.1982
R'F'L F'D'F'D L'B L F L'B'F²R 16,15 [SOO'] MG.1982
R'F²L'D'L F²B D B'D'FsL B L²D L F'R 22,19,18 [SS'O] MG.
R'D B D B R'U²R B'D'R²B'D'R 16,14 [SOH] MG.1982
R'D B R'U'B L U²L'B'U R'B'D'R 16,15 [SOH]
U'FsUsR F²R'DsR'B R²F'R U 18,16,13 [SOH]
R'F'L FaD'F D FsL'U F²U'R 16,15,14 [SO'H] Nánásy.1982
R'F'L BsD'F'D B'L'F U F U'F R 16,16,15 [SO'H] Nánásy.1982
B D L'D²R D'FsUsR U'L²U L'D' 18,16,14 [VSH] MG.1982
R'D'R²B R'F'R B'R²F R'D R F R F' 18,16 [VSO] MG.1982
? [VSO']
BsR'D B²D'R F²sU L'B²L U'Bs 20,16,13 [OHH']
B²D L'F'D²F L D'L'D F L²F'D'L B² 20,16 [OHH']
B²D L'F'D²L'F U L²U'F'L F L D'B² 20,16 [OHH'] MG.1983
B D R'B'D L F'D'L B²L'D F L D'B R D'B' 20,19 [OHH']
D'L F R U²L U²R²U²L'U R²U R'F'L'D 22,17 [VHO] MG.1982

Semi-regular ornaments - supplements

R F²B'D'BsRaDsF'R²L U' 16,14,12 [DS] MG.1982
B'D L²D'R'D L²U'BsLsD L 16,14,12 [DO] MG.1982
D'L B²L'F'L B²R'DsBsL B 16,14,12 [DO] MG.1982
R'U FaLsDsF'R'B R²F'R U 16,15,13 [DSO] MG.1982
R'F'L F'D'F'D F R'DsBsRaU 16,16,14 [DSO] MG.1982
R'F'L BsD'F'D B'L'B L F R'DsBsR U 20,20,17 [DSO'] MG.1982
U R'F²L DsBsL B'R²B R'F' 16,14,12 [DHO] MG.1982
U R'F²R B LsDsF'R²B R'F' 16,14,12 [DHO] MG.1982
FsU'RsU'R²sD²U'BsLsF Ls 20,17,11 [DSH] MG.1982
BsLsD U²RsU'R²sD RsU Bs 20,17,11 [DSH] MG.1982
B²R U²B²L'B'L F'LsDsB U'F L² 20,16,14 [DVS] MG.1982
B²R U²B²R'DsBsR'D L'F U'F L² 20,16,14 [DVS] MG.1982
B'L F'R'aDsBsU'L U R'DsL'U L²D R D' 22,21,18 [DVO] MG.1982
F²L'F R UaF'aRaD'L D'L²R'U²F²L 22,18 p20 Mark's Pattern 1 (K)
LsU FsD F²sU'FsU'F R'DsB R'F'LsU 24,22,16 [DSHH'] MG.1982
R'F'L F'D'F'D L'B L F R'DsBsR U 18,18,16 [DSOO'] MG.1982
? [DSS'O]
R'BsL F²R'DsR'B R²F'R U 16,14,12 [DSOH] Nánásy.1982
U'B L B L U'F²U L'B'U²L'F'LsDsB 20,18,16 [DSOH] MG.1982
R'F'L B²LsDsF'R B RsD'F R²F'U 20,18,15 [DSO'H] Nánásy.1982
D L B'L B L U'F L'F'L'U L'D' 14 [DVSH] MG.1982
D L U'L²U L'FsL F'L²B L'D' 16,14,13 [DVSH] MG.1982
R'D'R²B R'F'R B'R²F R'D L DsBsL U R 22,20,18 [DVSO] MG.1982
R'D B D L'FsU B U'BsLsU²R B'D'R²B'D'R 24,22,19 [DVSO] Nánásy.1982
? [DVSO']
B'L²F L'D'B'U RsB'D F D'B L B L'B D 20,19,18 [DOHH'] MG.1982
? [DVHO]

Ornaments composed from U2, U3 or U4

D F'UsL'DsF UsL²F'L DsF'LsD BsR'D B'R' 26,25,19 [DU3U4]
U L F'L DsF'LsD BsR'D LsU'L'U'F'aU'BsL F²U 28,27,22 [DU2U3]=[LU3]

Semiregular semi-ornaments

Even positions

RsD²F R²DsB²R BsD²L²U F²sU' 24,17,13 [WOS(1324)S'(14)(23)] (K)
p138 Mark's Pattern 5
D'F'D F DsB L'D L UsB'D'B R'F'D'F'D 20,20,18 [WORKS(14)] MG.1982
B R D²L'D R²D'L D²R'B R²B² 18,13 [WRR']
U'F²U F²R'B'U'F²sD B L'F²U'R²D 22,16,15 [WRR'S(1423)S'(1423)]
p158 Mark's Pattern 14
U'B²RaU²R'B'U L'B UsR'B U'R B'DsB²R²U 26,22,20 [WS(14)S'(23)] Walker
B'U'FaR U'R²U R'F'aU B 14,13 [OKK'S(14)]
B'D'RaB L'F²L B'R'aD B 14,13 [OKK'S(14)]
L'DsF D'R²D F'UsL 12,11,9 [ORKS(14)]
D R²U'aF'aR²FaR²U 14,11 [RK]
D R²sU²B D²R²sU²F D 18,11,9 [RK]
p181 Mark's Pattern 18
R'(D B D'B')^3 R 14 [RR']
FaR²sF'aU'F²UaF²U D² 18,13,12 [RR'S(14)(23)]
D'F²D'aR²sB²R²sD²U 18,11,9 [RR'S(14)(23)]
D FaR²F'aD²R'aB²RaD 16,13 [RR'S(14)(23)S'(14)(23)]
4 T's type 1 Nánásy.1982
D'B²RaF²UaB²U'aB²R'aD 18,14 [RR'KK'S(14)S'(23)]
(F²U F²sU B²)²Us 22,14,10 [RR'KK'S(1342)S'(24)]
p163 4 ARM Full
U'L'B'U'R²sD F L'R²D²F²U²sF²U' 24,16,14 [RR'KK'OS(12)]
p147 ML's 6 ARM Pattern (K)
U RaF²R'aU' 8,7 [RKS(14)(23)]
D FaR²F'aD' 8,7 [RKS(14)(23)]
U R'aB²RaU' 8,7 [RKS(14)S'(23)]
D F'aL²FaD' 8,7 [RKS(14)S'(23)]
U'R F²sL²F²sR'U 14,9,7 [RKS(14)S'(14)]
D L²D'aBaL²B'aL²U = D'RaB²R'aB²UaB²U' 14,11 [RKS(23)S'(23)]
U'R²UaR²D' 8,6,6 [KK'S(14)(23)]
D'F²DaR²sB²R²sU' 16,10,8 [KK'S(14)S'(23)]
U'FaR²F'aU²R'aF²RaU' 16,13 [KK'S(14)(23)S'(14)(23)]
4 T's type 2 Nánásy.1982
RsDsR UsF²LsD = SrSfD SbD²SlD 12,11,7 [S(13)S'(24)]
(U L²B²R²D)²L²R²B²F² 24,14,12 [S(13)(24)S'(12)(34)]
p165 2 Swap, 4 H full
D'R²F'aD²FaR²F²D 14,10 [S(14)(23)]
D F²R²F²D²R²F²R²D 16,9 [S(14)(23)]
D'R²FaU²F'aR²F²D 14,10 [S(14)S'(23)]
Sf²Sr²D Sf²D²Sr²D 20,11,7 [S(13)(24)S'(13)(24)]
Sr²Sf²D Sf²D²Sr²D 20,11,7 [S(13)(24)S'(13)(24)]
U'R²UaR²sD'aL²U 14,10,9 [S(14)(23)S'(14)(23)]
(D R²U )^4 16,12 p162 2 X, 4 H full
(F²sD F²sU)² 20,12,8 [S(134)S'(134)]
p170 2 edge swap + 2 H
R'B R²L'DsFsU RsB'D'L'D Rs 18,14,11 [DS(14)]
RaF²sR'aDs 10,8,6 [DWO]
(D R²FaU)^3 U²sR²U²sL² 30,21,19 [DWORK]
p178 2L, 2 Fours, 2 arm
D'L²FaD²F'aL²D²sF²U²D' 20,13,12 [DWOS(14)(23)]
U²F²D²U²F²Da = U F²U²D²F²D²U 12,7 [DWOS(12)S'(12)]
U F²D²sF²D²U 12,7,6 [DWOS(14)S'(14)]
F²U²RsD²sLsU²B²Us 18,12,8 [DWOS(12)(34)]S'(12)(34)]
U²F²R²sD²R²sD²F²Da 20,11,9 [DWOS(12)(34)]S'(12)(34)]
B'U'R F'U RsB'U R'B U'RsFaUs 18,18,15 [DO]
R D'B L'D F²sU'R B'U L D²sR²Us 22,17,14 [DO]
U R'B'U'F²sD B L'D F²R²F²U'F²D' 22,16,15 [DORR'] (K)
p93 Mark's Pattern 2
R F U FsR'F'R F'R DsB'L'R²D'F' 18,17,15 [DOS'(143)] MG.1982
D R²UsB²R²B RsD'R²D LsB'U' 20,16,13 [DOS(14)S'(14)] MG.1981
D R²UsB²U'R²B RsD'R²D LsB' 20,16,13 [DOS(14)S'(14)]
p81 Snake type 1
D R²UsB'LsB'R'B RsD'R D B'U' 18,17,14 [DOS(14)S'(14)] MG.1981
D R²UsB RsB R B'LsU R'U'B U' 18,17,14 [DOS(14)S'(14)] MG.1981
F²sLsB'DsL²F²L'FsU B²D' 20,15,11 [DS(13)(24)S'(13)] (K)
p146 Mark's Pattern 9

Odd positions

R D'L²B L B'L U²R'F R U²D R' 17,14 [OK]
R²F²D F D'F L²B'U B R²s 17,12,11 [KS(14)]
L²F L'D'L F'L'D F'D'F'D F L' 15,14 [KS(14)]
L F'D'aF D F'U F²D'F D F'L' 15,14 [KS(14)]
F²D F²D L²D F²D'F²D'L²D²F²D'F²D' 25,16 [KS(14)]
R²U'F'U F'L²B D'B'L²F²R² 17,12 [KS(13)]
F'D'F L²B'U B L²F²D F² 15,11 [KS(12)]
RaDaR'D'R U'R²D R'D'Rs 15,14,13 [KS(23)]
D²B²R²D'R'D R'B²L U'L'D² 17,12 [RS(13)]
U²F²L²D'L'D L'F²R U'R'U² 17,12 [RS(13)]
U R'F R'B'R'B R'F'U'R U R'U² 15,14 [RS(13)]
U R'B U'B'U'B U R U R'B'R U² 15,14 [RS(13)]
U²L²U B²U'B²D L²D'B²D B²U² 21,17 [RS(1324)]
R D'F²D F'R F UsF DsF'R²D F D'R D F'D' 23,21,19 [ORKK'S(14)(23)] MG.1983
D'RaB²L'U'aL²B L B'L U²R'F R DsR'D 23,20,19 [ORR'K'S(23)S'(14)] MG.1983
F²D²sF R'D R²D'R F'U R²U²R²D²F² 25,16,15 [ORR'K'S(23)S'(14)] (K)
p119 Mark's Pattern 3
R U'F R'B'D²R'U'BsLsD B L U'R'U'F U'Ls 23,22,19 [DK]

Cyclic patterns

R²sU F²sU²R²sD'F²sD² 22,12,8 crosses
R²sD²F²sD R²sU²F²sU' 22,12,8 crosses
U R²sU'R²sU²R²sD'R²sU' 22,13,9 crosses + 2 X's
R'B'RsF'R'SdR F LsB R 14,14,11 4 U's MG.1981
F R'B'D²L'UsB D²R F L' 14,12,11 p112 4 U order 4
R'B'RsF'R'U R F LsB R 13,13,11 4 T's MG.1981
R²sF²sD'F²sR²s 17,9,5 4 Y's
D R²sDsR²sU'a 13,8,5 4 Y's + 2 X's
FsL F²L²UsB U²RsB²D L²U' 20,15,12 p114 3 ARM Order 4
U'B'R'U F'UsL U'F R'U R²sD'L²D 20,17,15 4 X's & 2 K's (K)
p122 Mark's Pattern 4
D'R F R'F²B L D'F U L'B R²sF²R 20,16,15 4 O's & 2 K's
p144 Mark's Pattern 7

Three-color regular patterns

R²sUsRsBsUs 12,10,5 blossomes
B R'D²R D'B²D R'D²F²R U'B²U R'F²R F (F) 24,18 6 Stripe type 1
U F B R DsRsD'R'aB R²D²R²B²R 21,17,15 p120 6 Stripe (1)
L U R'B²R B'U²B R'B²D²R F'U²F R'D²R U'R 26,20 6 Stripe type 2
RaD R'aD F'aU'FaRaU'R'aD'F'aD Fa 22 diagonals (4 Peak flip)
U'F²L²B²D²F²R'UaF'LsBsR U' 21,16,14 p69 Tetra Peak exch (K)
D'R'BULsB'UB'U'BL'BLB'UB'U'BRsDB'DsF'UsLB 30,30,26 giant meson 1
L D R²D'L²U B'D'B D'R'D R DsL D'B²D 22,19,18 giant meson 2
R²L'DBR'D'BLBL'D'B'D²LDL'U'FD'F'RFL'FLF²R'D²U some about g. meson 1
DFRsU'B'D'R'aD'LsBDFD²F²DF'R'B'L'DLBF²RD'R²D some about g. meson 2
RaDaR'aF'aDaFa 4 Peak flip + 4 twists (Pinwheels)
U'L'B L'B'L'D²U'FsRsF'U F D F'U B 20,19,17 [D'HOO'] (see [HOO'])
LsD L'DsF D'B'RsD²U' 14,13,10 [D'H]
F R²sU²sF²B'R²U F²sR²sU²D'L² 28,16,12 p82 8 Crn Twist 1
U R U'R D²B²U'L'D R FsUaL²U²sB² 24,18,16 [DV]+chessboard s.p. (K)
p125 ML's Multicolor 1
B²D'F²U'L²D²F²U'F R B U²F²R F²D FsU'F' 28,20,19 Triple Threes (K)
U B²D'L²F²R²U'B U'L D F²L U'B'F'R²U'F² 26,19,19 Orthogonal bars (K)
UsRsFsU L UsB'DaB'D²sF U²R U²sL'D²U 30,24,18 (similar to [D'HH']

Three-color regular ornaments

B'L'D L'D'L'F R FsUsF'D'F RsU'F B²D 22,21,18 [D'OHH'] (see [OHH'])
B²R²D²R²B'D²B'L²F U²L'D L D²R'F L²F²D B' 30,20,20 Treep's Skein (K)
U²B'D²B'U²B²U²B'D²B R²L B R D'R F²D U²R B 30,21,21 Z-snake type 1 (K)

More-colored regular patterns

F²D'F²L²U'F²R²F²D F'U²LsFsU Fs 25,18,15 Perry's Pinwheel (K)
D²B²R²F²R²D²U L²F²D RaF'L F'aD'B²L²U' 30,20,20 Six L's - 6 colors (K)
U²L²U L²D'L²U B²U'F'aRsF'D²L²U'B'D B 27,20,19 Two diamonds (K)

More-colored nonregular patterns

B R'D²R D'B²D R'D²F²R U'B²U R'F²R B' 24,18 4 Stripe
D RaD²F LsBsR'D'aB U²RsB² 20,17 p92 4 Stripe (Full)
R'B'L²BD'R²D B'L²U²B U'R²U B'U²B R 24,18 4 Stripe + 2 X's MG.1982
R²F²U'L²U²F²U'F²L²F²R'F R²B L F'R²B'R D²R² 33,21,21 Four T's (K)
R'U'B'R²B R B U'FsU F'L'F'L²F U L 20,18,17 2 Peak twist MG.1983
U R'F'R²F D R U'R D'R²L'U'RaFaU'F'a 22,20 3 Peak twist MG.1982

Flips and twists

(U R'F R )^5 20 p171 6 Edge Flip
(F R'D'R)^3 (L'B D B')^3 24 6 flip
(RaUaFa)² 12 8 edge flip
R U'R²U'R U'aR U'R'D²R'U'R U'a 18,16 p183 6 Twist
U F²L F²sU²sR'L²B²U²D'F²sR²s 28,16,12 p155 8 Crn Twist 2 (K)
(L R²F²B')^4 24,16 p156 8 Crn Twist 3
RaD²B'L²F²R²DsR'D²F'aD'F²D'R²U'F²D' 28,20,19 p3 12 flip (K)
D F²U'B²R²B²R²L B'D'F D²F B²U F'RaU²F' 28,20 p6 12 flip, 8 twist (K)
FsR UsB²R²B'LsF²sU'F²D'F²sD'R²D' 28,20,15 p139 6 X + 12 flip (K)
B'L D L F'U'aL B'D'F'RsF'UaL²UaB² 22,20,19 p139a (K)
F R'DsR'B D'F²R²L F R'B'L D²B²U'R²sD'R²s 30,22,19 p141 Superfliptwst + 6X (K)
F R L²U'R²L'U'D²R²F D B D F²U'R'D'F²D²L² 28,20 p141a (K)

Patterns possible by disassembly

U L U L'U'F L'U'F'U'F'U L U L²U'F'L' + FLU+ 19,18 2 Peak exch MG.1983
R'D²B²L B L'B D'R D' + BDR- 12,10 1 Peak twist MG.1982
R'D R'B U'B U B²R²D' + BDR- 12,10 MG.1982
R'D R'B R B²D B D'R D' + BDR- 12,11 JF.1983
R'D R'B R B'R D'R F'R'F + BDR- 12 MG.1982
F D'F'D R'D B'D B D'R D' + BDR- 12 MG.1982


U'R D BsR'U'L Ds + (UR,LF+) 10,10,8 3 U's + 3 O's MG.1982
L'UsL'U R FsD'R'U B + (UF,BL+) 12,12,10 3 U's + 3 O's MG.1982
D'R'aD RsF'aUsR FaL + (UR,BD+) 14,14,12 3 U's + 3 O's MG.1982
F U RsB'D'F'RsF'LsD F + (RD,RF) 14,14,11 6 U's type 1 MG.1982
U'F U RsB'D'F'RsF'LsD F R + (UR,FR) 16,16,13 6 U's t2 MG.1982
U'F U RsB'D'F'RsF'LsD F R + (UR+) 16,16,13 3 U's + ring MG.1982

Regular semi-ornaments

L D R²D'L²B'D'B UsR'D R DsL D'B²D +(LDF,LFU) 22,19,17 cube within a cube

Semiregular semi-ornaments

R F U F²U'R'F' + (FD,RD+) 8,7 [VRKS(14)]
U'B²L'F D'F'L B²R U R + FU+ 13,11 [VRS(14)]
F²R'D R D'R F²D R'D'R' + (FD,RF) 13,11 [RS(14)(23)]
F²R'D R D'R F²D R'D'R' + (FD,FR+) 13,11 [VRS(14)(23)]
R F U F²U'R'B'D'F'D BsR'F R + FD+ 16,15,14 [VRKS(14)(23)]
D²F UsL'D²L²FsU²D FsL' + (BL,DL) 18,14,11 [D]
R'F L DsBsD LsB'U'R'U Ls + (DF,UL) 16,16,12 [D]

Cyclic patterns

RF'DR'U'B'UB'R'B'RBR'D'R'FR'Us + (LUB,LBD) 19 O's MG.1982
B'D R D'RsF R'F'R'F'UsL B R + (BU,LU) 16,16,14 O's MG.1982
F L B UsR'U'B'U FsR'B R F'L' + (BU,LU) 16,16,14 O's MG.1982
R'B D F'RsU F'D'F'D'LsB U F + (LU,LB) 16,16,14 O's MG.1982

Simple patterns

It is quite a qood excercise to try to get back the Cube from these positions. The number at each sequence means a number of 'long moves' like Fs,R²,Da. Three characters in the column 'position' describe what you can see on faces F,R,U. Only position with O,H,I,X,+,_ on all faces, where O,I,+ occur in pairs, (in parentheses in the column 'position') are possible.

slice movesposition
R²D'sR²sD'sL² 6 (H,H,H)
FaR²F²sD²sL²F'a 8 (H',H,H)
R²sF²sD²s 6 (X,X,X)
RsFsRsFsRsFs 6 (X,X,X)
RsF²sD²sRs 6 (X,X,X)
R²sF²R²sB² 6 (_,_,H)
D²RsF²sR'sU² 6 (_,_,H)
DaF²sD'sF²sD² 7 (_,_,X)
R²sF²R²F²sR²F² 8 (_,_,X)
R²sD'sF²sD's 6 (O,O,_)
RsD'sF²sD'sR's 6 (O,O,_)
D²FsD²sFsD² 6 (O,O,H)
D²R²sF²sD² 6 (O,O,X)
R²F²DsF²sDsB²R² 8 (H,H,_)
RaD²sR'aF'aD²sFa 8 (H,H,_)
(F²B²R²L²U²)² 10 (H,H,_) p160a
D²sRsF²sR's 6 (H,_,H)
F'sR'sFsR'sF'sRs 6 (H,_,H)
FsD²F²D²sF²D²Fs 8 (_,H,H)
R²B²R²sB²L² 6 (I,I,_)
R²s 2 (I,_,I)
R²F²R²sF²R² 6 (_,I,I)
U²RaD²sRaD² 6 (_,I,I)
R²F²sR² 4 (I,I,H)
R²FsD²sF'sR² 6 (I,H,I)
DsFaD²sFaDs 6 (I,H,I)
RaD²sRa 4 (H,I,I)
R²B²DsF²sD'sB²R² 8 (H',I,I)
F²D²R²sF²sU²B² 8 (H',I,I)
R²sF²s 4 (I,I,X)
RaD²sRsD²sR² 7 (I,X,I)
R²FaR²sFaR² 6 (X,I,I)
R²sDsR²sDs 6 (H,H,X)
RsFsR²sFsRs 6 (H,H,X)
R²F²sD²sL² 6 (H,X,H)
R²F²sR²F²D²sB² 8 (X,H,H)
DsRaU²R'aD'sF'aU²Fa 8 (+,+,_)
FaUaR²sUaFaU²s 8 (+,+,_) p16a
R²F²R²DsF²R²F²Us 8 (+,+,_) p16c
R²D²sF²D²sF²R² 8 (+,+,H)
D²sR²D'sR²sD'sL² 8 (+,+,H)
R²sD'sR²sDs 6 (+,+,X)
RsF'sR'sFsRsF's 6 (+,+,X)
R²F²R²sF²L²D²s 8 (X,X,_)
D²sR²F²sR² 6 (X,X,H)
RaD²R'aFaD²F'a 6 (U,U,_)
RaD²R'aF'aU²Fa 6 (U,U~,_)
D'aB²DaL²D²R² 6 (U,U',_)
R'aD²RaF²D'aR²DaF² 8 (Z,Z,_)
R'aD²RaF²DaR²DaB² 8 (Z,Z',_)
R'aF²D'aL²DaF²RaD² 8 (Z',Z',_)
D'R'aD RaU²R'aD'RaD' 9 (Z',Z',_)
F²sDaF²sD'a 6 (_,H,X)
R²sF'aD²sF'a 6 (_,H,X)
L²F²R²sF²D²sL² 8 (H,X,_)
DaF²sD'a 4 (_,O,I)
D²R²sU² 4 (O,_,I)
U²R'sD²sRsD² 6 (_,O,+)
F²R²sF²R²s 6 (_,I,+)
F²R²DsR²sD'sR²B² 8 (I,+,_)
DsF²sDs 4 (H,O,I)
D²R²sF²sD²F²s 8 (O,H,I)
D²R²sU²R²F²sL² 8 (O,I,H)
F²RaD²sRaF² 6 (H,I,O)
RsF²D²sB²R's 6 (H,O,+)
DaF²D²sR²sB²Da 8 (O,+,H)
R'sD²sRs 8 (H,I,+)
R²F²sD²sL²D²s 8 (+,I,H)
RsU²F²D²sF²U²R's 8 (+,I,H)
R²D'sR²sDsR² 6 (I,+,H)
R²F'sR²sFsR²D²s 8 (+,H,I)
R²sF²D²sB² 6 (X,O,I)
F²U²F²sU²R²sB² 8 (X,I,O)
R²F²sR²F²D²sF² 8 (X,O,+)
FaR²sFaR²s 6 (X,I,+)
DsFaD²sFaD's 6 (X,+,I)
F²L F²U²sB²R B² 14,8 4 T's
F²L B²U²sF²R B² 14,8 4 T's

One little square of opposite color

RsU²RaFaU²F'aR² 14,11,10 [E4]
L²D S²rD²S²rD L² 16,9,7 [E4]
D²F²U²L²F²L²U²F²L²D² 20,10 [E4]
RaD'aB²D'aR²D²Ls 14,11,10 [E6]
U R²F²sL²D'BsL²BsD² 18,12,9 [E6]
F²U²L²D²F²L²F²D²F²U²F²L² 24,12 [E6]
B²U²R²B²R²B²L²B²U²B²R²s 24,12 [E6]
B²U²B²L²B²R²B²R²U²B²R²s 24,12 [E6]
R D'L B L²D²R F R'D²L B'D R' 17,14 [C2E2]
D'L²F²U F²U'F²L²U'L²D F²D'L²D 23,15 [C2E2] Domino alg.
U R'F'R²F R U²R'F'R²F R U 16,13 [C3]

Two corner little squares of opposite color

RaD²B²D²B²D²LsB²L² 18,11,10 [C3+3]
FaU²FsR²U²R²U²R²F² 18,11,10 [C3+3]
F²D²R²D²F²D²F²R²F²D² 20,10 [C3+3]
D'aFsD²BsUsFsD²Bs 16,14,9 [C2+4]
R²F²D²R²F²D²R²F²D² 16,14,9 [C2+4]
BsU²FsR²U²R²U²R² 16,10,8 [C6]
U²R²U²F²U²F²R²F²U²F² 20,10 [C6]

Odd simple patterns

F'D²R²F R F'R U²L'B L D²sF D² 21,15,14
R B'D RaD'L'D R'D²L D'L'D B R'D² 19,17
F²R²U²F²R²U'R²D²B²U'L²U²L²B²U 27,15 p123 Cube in a cube 2

Algorithms signed (p..) where .. replaces a number were taken from Michael Reid's PATTERNS.TXT - August 24, 1996.

Algorithms with (K) as the author were probably produced by a computer program based on Kociemba's 2-step algorithm. The authors of those algorithms are not known to us. Please, if you know who obtained those algorithms for the first time, let us know. Thank you.

Algorithms signed (MG.) are Mirek Goljan's results, JF. denotes Jessica Fridrich.