Corner Dual-Sided Rubik's Cube Mosaic: CDSI Method

[academicmaslow]

Hey everyone,
Since 2020 I experiment with dual-sided mosaics of verious types.
Now I'd like to share my recent work on a new class of dual-sided patterns on a Rubik's cude. I called it Corner Dual-Sided Isomorphic (CDSI).
The idea is the following: take two adjacent faces of the cube (Front and Right) and place a two-color pattern on each. The two patterns are geometrically identical – the same arrangement of stickers – but the colors are inverted using opposite color pairs (red/orange, blue/green, white/yellow). So you get a mirror in color, not in geometry.

The whole system content 12 288 possible patterns

• 256 distinct half-patterns on a single face (the center is fixed, so 2⁸ variable stickers). The center can also have two colors. So we have 512 shapes.
• 24 valid color combinations (12 adjacent face pairs × 2 orientations).

I solve each of 256 pattern by hand to found the whole state of the cube. Put it into Cube Explore (developed by Herbert Kociemba) that generated optimal (or suboptimal) solution for every patern.
So I create a database of 256 algorithms, each 14 moves or fewer.

Now anyone can build corner mosaics (even without cubing skills - you need to know only Singmaster's cube Notation):

• Choose a binary image.
• Split it into 3×3 blocks.
• Choose one of the 24 color schemes.
• Apply the algorithms to cube.
• Repeat cube by cube.
• Mosaic is done.

As you can see visual effect when scaled up to mosaics of dozens or hundreds of cubes:

• Front view – a blended mixed-color image.
• Viewed from one diagonal (~45°) – resolves into a clean two-color pattern from one face.
• Viewed from the opposite diagonal – reorganizes into a different two-color image using the inverse color pair on the other face.

Here is a video with my presentation at the Bridges 2026 Conference on Mathematics and the Arts Conference.

Full paper with the methodology (and a list of algotrithms) is availible at Bridges 2026 web page: https://archive.bridgesmathart.org/2026/bridges2026-253.html#gsc.tab=0

If anyone here has experimented with adjacent-face patterns before?

 

[bcube]

If anyone here has experimented with adjacent-face patterns before?

I have no experience in making cube mosaics or creating pretty patterns, but there is a whole solving method of which I am a big fan having a similar visual effect.

If anyone is interested, a 6-color 3x3x3 cube presolved as a 3-color cube has the following number of cases/states:

Corners:

4! Tetrad 1​

4! Tetrad 2​

Edges:

4! M slice​

4! E slice​

4! S slice​

So (24x24)x(24x24x24)/2 = 3981312 cases/states in total (dividing by 2 because of parity).

What I think about your design?

 

[academicmaslow]

Hi bcube, thanks for bringing up the 3-Color Method.

My CDSI patterns are elements of the subgroup generated from the solved cube by double moves.
This relates directly to the 3-Color Method.

I think the intersection of these two state spaces is worth investigating further in the context of CDSI-mosaics.

 

[bcube]

Hey academicmaslow,

My CDSI patterns are elements of the subgroup generated from the solved cube by double moves.
This relates directly to the 3-Color Method.

Careful with that statement, I believe that's not the case. See the "3x3x3 phase 2 with unlimited solution length" section here. We need to distinguish between HTR states and fake HTR states on a 6-color cube presolved as a 3-color cube: fake HTR states can not be solved by half-turns only.

 

[academicmaslow]

Hey academicmaslow,



Careful with that statement, I believe that's not the case. See the "3x3x3 phase 2 with unlimited solution length" section here. We need to distinguish between HTR states and fake HTR states on a 6-color cube presolved as a 3-color cube: fake HTR states can not be solved by half-turns only.

Good catch, seems you're right.