Virtual Cubes

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.

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Superflip
Centre

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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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