# Virtual Cubes

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### 8 Color Cube 1

The '8 Color Cube' is solved, when all colors and numbers are represented only once per face. In contrary to a regular Rubik's Cube a total of 581'952 valid solutions exist.

This cube design was invented by Paul Kobayashi.

Tip: You get an other valid solution if you apply the Superflip pattern.

#### The number of possible positions

The number of possible positions for the 8 Color Cube is 7! corner permutations × 12! edge permutations × 211 edge orientations = 4'944'216'195'072'000 ≈ 4.9 × 1015.

The 8 Color Cube has eight corners and twelve edges. Since the centres are all identical, a corner can be fixed instead of the centres. With the centres freely rearrangeable, odd permutations of the edges are possible as well.

#### Valid solutions

In May 12, 2020 Dutch mathematician Michiel de Bondt computed the total number of valid 8 Color Cube solutions. According to his discovery there are a total of 581'952 positions, including the initial state, that displays all colors and numbers only once per face. See the 'Domain of the Cube Forum' article An unsolved problem: how many solutions are there to the 8-Color Cube? for further informations.

#### SuperflipCentre

Algorithm Michael Reid 06.08.1997, Michael Reid 07.08.1997 (Cube Lovers)
U R2 F' R D' L B' (R U')2 D F' U F' · U' D' · B L' · F' B' · D' L' (23 ltm, 23 ftm, 24* qtm)

Algorithm Dik T. Winter 18.05.1992 (Cube Lovers)
F B · U2 R F2 R2 B2 · U' D · F U2 · R' L' · U B2 D R2 U B2 U (20 ltm, 20* ftm, 28 qtm)

Algorithm Herbert Kociemba 14.05.2010
CD CR2 · MR2 U' R2 D' MF MR2 U MR U2 F2 D' MF MR2 U' R2 U' (16* ltm, 22 ftm, 32 qtm)

Note
This was the first known valid solution apart from the initial state of the 8 Color Cube.

#### Super Inversion

Algorithm Michael Reid
F U' F L' F' D F' · R' L · U' D · F · R' L · D R' D L' F' L U' L (22 ltm, 22 ftm, 22* qtm)

Algorithm Michael Reid
F B · R · F2 B2 · U2 D2 · L' U2 R2 U2 · F B (U2 R2)2 (17 ltm, 17* ftm, 28 qtm)

Algorithm Herbert Kociemba 2010
CD' · MF2 D2 MR2 D' F2 MD' R2 U2 L2 F2 U2 F2 R2 U' (14* ltm, 17* ftm, 30 qtm)

Note
Valid 8 Color Cube solution found by Walter Randelshofer.

#### Super Inversion + Superflip

Algorithm Walter Randelshofer 2017
U F U R' U' · F B2 · L' F' D F · R2 L' · U' · R L · U D · F B (20 ltm, 20 ftm, 22* qtm)

Algorithm Walter Randelshofer 2017
B2 D F2 D' · F' B · R D2 F2 R · U' D' · F · U2 D2 · R' L · U' (18 ltm, 18* ftm, 24 qtm)

Algorithm Walter Randelshofer 2017
CF · MD' MF' L' F2 · U' D' · B MR2 D2 MR' U2 F' · R' L' · U' (15* ltm, 19 ftm, 24 qtm)

Note
Valid 8 Color Cube solution found by Walter Randelshofer.

#### 4 Small Edge Triangles

Algorithm Michael Reid
R L · F' D · F B' · U D' · F' D B U' · F B' · U D' · B U' · R L (20 ltm, 20 ftm, 20* qtm)

Algorithm Michael Reid
L' · U' D' · L' · F B · L' · U2 D2 · F2 B2 · R' · U D · R' · F' B' · R' (18 ltm, 18* ftm, 22 qtm)

Algorithm Herbert Kociemba 2010
CD2 MF2 · D2 MR2 U' B' MR MD' B R' MF' MD R U' (13* ltm, 19 ftm, 24 qtm)

Note
Valid 8 Color Cube solution found by Walter Randelshofer.

#### 4 Small Edge Triangles + Super Inversion

Algorithm Walter Randelshofer 2017
F B · U · F B · U' D · F' B' · U' D · R' L' · F' B' · U · R' L' (18 ltm, 18 ftm, 18* qtm)

Algorithm Walter Randelshofer 2017
F B · U' D' · R' L' · F' · U2 D2 · R2 L2 · F' · R2 L2 · F2 (15 ltm, 15* ftm, 22 qtm)

Algorithm Walter Randelshofer 2017
CD2 · L2 MF2 R MF2 MD2 R · F B · U D · R' L' (12* ltm, 15* ftm, 22 qtm)

Note
Valid 8 Color Cube solution found by Walter Randelshofer.

#### Solution 1

Algorithm Walter Randelshofer 2017
D L' B' U · F2 B' · U D' · F' U' L' B D' F' L' F' · R L · U (19 ltm, 19* ftm, 20* qtm)

Algorithm Walter Randelshofer 2017
CF CR · B' U MR B2 MD F D2 F L' B MR' U2 F2 L' MD R' U2 (17* ltm, 21 ftm, 26 qtm)

Note
Valid 8 Color Cube solution found by Peter G. Tchamitch.

#### Solution 2

Algorithm Walter Randelshofer 2015
R' F' R' U (R2 F2)2 R · U D' · F D' (U L)2 D' (18 ltm, 18* ftm, 22* qtm)

Algorithm Walter Randelshofer 2017
CF CR · MF D2 MR U' F L2 F R MD' L' MF D2 R D F2 U' (16* ltm, 20 ftm, 24 qtm)

Note
Valid 8 Color Cube solution found by Peter G. Tchamitch.

#### Solution 3

Algorithm Walter Randelshofer 2017
D' R' U L' B' L' U F U F' D R2 · F' B' · D' L' B' D R' (19 ltm, 19 ftm, 20* qtm)

Algorithm Walter Randelshofer 2015
B R' F D' L D B' · U D2 · L' F' U2 L' B2 L B' L2 U (18 ltm, 18* ftm, 22 qtm)

Algorithm Walter Randelshofer 2017
CD' CR' · MF L B' MR F' U R2 MD2 F' D F U2 R' U' B2 R U2 (17* ltm, 20 ftm, 26 qtm)

Note
Valid 8 Color Cube solution found by Peter G. Tchamitch.

#### Solution 4

Algorithm Walter Randelshofer 2015
L' F U' R2 B L' D' F' U L2 D F' L D' R' D' R U' · CD (18 ltm, 18* ftm, 20* qtm)

Algorithm Walter Randelshofer 2017
CR2 · U L2 U2 B' D' B' D2 MF R' F D MF L2 D2 R MD2 · CD (16* ltm, 19 ftm, 26 qtm)

Note
Valid 8 Color Cube solution found by Peter G. Tchamitch.

#### Solution 5

Algorithm Walter Randelshofer 2017
L U B' · R L' · D' L2 B L' B' R' D B' · U' D' · L U' F U (19 ltm, 19 ftm, 20* qtm)

Algorithm Walter Randelshofer 2017
U R' D' B R D F2 R' B D B2 R D2 F' D2 F U' R (18 ltm, 18* ftm, 22 qtm)

Algorithm Walter Randelshofer 2017
CD2 · F D' L' · U D · MR2 B2 L' U' MF2 D L' D F' U2 R' (16* ltm, 18* ftm, 24 qtm)

Note
Valid 8 Color Cube solution found by Peter G. Tchamitch.

#### Solution 6

Algorithm Walter Randelshofer 2017
R · F B- · U' L' · U D · B D' · R' L' · U' L F' U F · U D2 · L' · CD (19 ltm, 19 ftm, 20* qtm)

Algorithm Walter Randelshofer 2015
L' B R B' · R2 L' · F' U2 · R' L2 · D' F2 · U2 D' · L' B L' · CD (17 ltm, 17* ftm, 22 qtm)

Algorithm Walter Randelshofer 2017
CF' CR' · D L' MF L MF MD2 B R F MD' MR' U' F D' L2 D' · CD (16* ltm, 21 ftm, 24 qtm)

Note
Valid 8 Color Cube solution found by Peter G. Tchamitch.

#### Solution 7

Algorithm Walter Randelshofer 2015
D F2 D' F2 L U2 L2 U' R' F R D' R' D' · F2 B' · U · CD (17* ltm, 17* ftm, 22* qtm)

Note
Valid 8 Color Cube solution found by Peter G. Tchamitch.

#### Solution 8

Algorithm Walter Randelshofer 2017
R F · R L' · B L' U' F L U' F' R' F' L F L D' R' F U · CD' (20 ltm, 20 ftm, 20* qtm)

Algorithm Walter Randelshofer 2017
R F' L' D' F · R2 L · B' U · F B2 · L2 F' R · F2 B · L U · CD' (18 ltm, 18* ftm, 22 qtm)

Algorithm Walter Randelshofer 2017
CF' · B' · U' D2 · R' U' B' U2 R' U2 B' L MF2 R MF' R2 U · CD' (16* ltm, 18* ftm, 24 qtm)

Note
Valid 8 Color Cube solution found by Peter G. Tchamitch.

#### Solution 9

Algorithm Walter Randelshofer 2018
D' F' U R' B' · R2 L' · B2 L B' U2 L' B' U2 F' D' B R · CR' (18 ltm, 18* ftm, 22* qtm)

Algorithm Walter Randelshofer 2018
CD CR2 · R MD B2 R B' MD2 B' D L2 MF2 D' F2 U L2 F D2 · CR' (16* ltm, 19 ftm, 28 qtm)

Note
Valid 8 Color Cube solution found by Walter Randelshofer.

#### Solution 10

Algorithm Walter Randelshofer 2018
R' · F B · D F' U' F2 D L' D2 R F' R U L2 D R2 U · CD (18 ltm, 18* ftm, 22 qtm)

Note
Valid 8 Color Cube solution found by Walter Randelshofer.

#### Solution 11

Algorithm Walter Randelshofer 2018
U2 R D2 B R2 · U2 D2 · B2 L D F2 D2 F' R' B2 U' R' · CD (17 ltm, 17* ftm, 26 qtm)

Note
Valid 8 Color Cube solution found by Walter Randelshofer.

#### Solution 12

Algorithm Walter Randelshofer 2018
B' U B2 R2 B2 D2 L D' F2 R2 U B2 D' L2 B' R2 B2 D (18 ltm, 18* ftm, 28 qtm)

Note
Valid 8 Color Cube solution found by Walter Randelshofer.

#### Solution 13

Algorithm Walter Randelshofer 2018
B2 U' B · U D' · B2 · R2 L' · F2 R' U L' D' L B' U' B2 · CD (17 ltm, 17* ftm, 22 qtm)

Note
Valid 8 Color Cube solution found by Walter Randelshofer.

#### Solution 14

Algorithm Walter Randelshofer 2018
R2 B' R F' D' F R · F2 B2 · D L U2 F2 U' F L' B' R2 (18 ltm, 18* ftm, 24 qtm)

Note
Valid 8 Color Cube solution found by Walter Randelshofer.

#### Solution 15

Algorithm Walter Randelshofer 2018
F' D L' D2 F' R2 U' B' R2 D2 F2 U2 R' U R2 U' L2 U (18 ltm, 18* ftm, 26 qtm)

Note
Valid 8 Color Cube solution found by Walter Randelshofer.

#### Solution 16

Algorithm Walter Randelshofer 2018
R2 F2 D B2 U L2 D F2 U · F' R2 U' R B2 L' D U' R D2 F' (20 ltm, 20 ftm, 28 qtm)

Algorithm Walter Randelshofer 2018
R2 D' · F B · D2 L2 D2 L B D F R D' F' U R2 B L2 (18 ltm, 18* ftm, 24 qtm)

Note
Valid 8 Color Cube solution found by Walter Randelshofer.

#### Solution 17

Algorithm Walter Randelshofer 2020
F2 · R2 L2 · D' L2 U L2 D' R2 U F2 D' L2 U' · F' B' · L F · U2 D2 · R2 L2 · B' U2 (24 ltm, 24 ftm, 37 qtm)

Note
Valid 8 Color Cube solution found by Peter G. Tchamitch.

#### Solution 18

Algorithm Walter Randelshofer 2020
D' R2 U' R2 D2 F2 U B2 D B2 L2 B2 U' B' D2 R · U' D · R' L · D' R2 F' R2 · CD (24 ltm, 24 ftm, 35 qtm)

Note
Valid 8 Color Cube solution found by Peter G. Tchamitch.

#### Solution 19

Algorithm Walter Randelshofer 2020
D2 R2 B2 D B2 L2 U2 R2 D L2 B2 R' B2 U R2 B' D2 L · U D · R' F2 (22 ltm, 22 ftm, 35 qtm)

Note
Valid 8 Color Cube solution found by Peter G. Tchamitch.