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When it comes to stickermodding or shapemodding, I never liked the concepts where a twisty puzzle becomes under-determined. That means, when pieces have no determined orientation and/or placement.
Therefore, I always liked the Rubik's Domino, where the cubies of one face have fully determined placement by looking at only one side, but no additional placement information on the side faces of the cubies. The other interesting feature of the Rubik's Domino is the two-color design, where the color of the cubies determines, to which half of the puzzle a cubie belongs.
I managed to get two original vintage Rubik's Domino, but decided to recreate them using current cuboids with better turning quality.
Since then, I had been thinking about how to implement these features on twisty puzzles other than 3×3×2 for a long time, until the point where I fully understood the whole concept.
The original concept was used on "Rubik's Domino", a 3×3×2 Twisty Puzzle Cuboid invented by Ernő Rubik. The original name was "Bűvös Dominó", which translates to "Magic Domino". Please note that the text on most (if not all) original boxes does not represent the correct Hungarian letters with long ű and short ö. The dot patterns shown on the boxes don't match, either.
There have been many discussions on how the cubies of the two halves of the Rubik's Domino should be arranged. I have seen photos by reputated speedcubers, where the opposite side was not solved correctly.
The correct solved state for the Rubik's Domino is a sequence from one to nine in lines filled left-to-right, arranged top-to-bottom. The domino patterns on the "leading" face show forward slanted two and three, and a "U" shaped number seven. The opposite side shows a mirror image of the leading face with the sequence right-to-left, top-to-bottom.
For more information and examples, see The Domino Project - The Vintage Rubik's Domino .
To put it simple: The Domino principle is a combination of indicating the permutation on a plane using a sequence, and the placement perpendicular to that plane by color.
The following list shows the rules of the Domino Principle, which I established during my various Twisty Puzzle Domino projects, starting with The Domino Project - Raising Domino to the Next Level: 3×3×3 Domino Cube . Maybe one day, I will rephrase these rules into the "laws" of the Domino Principle.
Two opposite faces are the "main" faces.
One main face is the "leading" face, where the sequence is distributed left-to-right, top-to-bottom.
If the leading face has a rectangular shape, the orientation giving the longer line length should be used.
The face opposite to the leading face shows the mirror image of the leading face. Actually, the image on the leading face runs along a perpendicuar axis to the opposite face.
The sequence uses domino dot patterns similar to the patterns used on the domino tiles.
The color of the cubies indicates to which half a cubie belongs.
If the puzzle has an odd number of layers between the main faces, the middle layer should have some kind of neutral color. If this is not an option, the middle layer should have the color of the leading face.
The outer layers have no marks at the side faces of the cubies, since placement and orientation is already given by the dots on the outer faces.
The cubies on the inner layers inherit the number given by the opposite cubies, i.e. the projection between leading and opposite face.
Each cubie number is only displayed once.
The numbers of inner face cubies should be displayed in such a position,
where the longest consecutive sequence is obtained on a common side.
With a 3×3 leading face, for example, 1-2-3 and 7-8-9 should each be shown on a common side. Numbers 4 and 6 are displayed on one side each, the inner number 5 relates to the core, and is not shown at all.
The orientation of the dot pattern on inner face cubies should be in a way as
if you would rotate the cubie of the corresponding face towards that side.
The middle layer should inherit the orientation from the leading face.
A "classic" Twisty Domino Puzzle should have black cubies with white dots, and white cubies with black dots. In case of an odd layer count, the middle layer should be clear with transparent dots.
The dots, and/or the main faces can have the same color,
as long as the cubies still indicate to which half they belong.
If the main faces have the same cubie and dot color, a special case arises. The placement of the centers is not determined, but you can easily exchange opposite centers on such cuboids.
The cubies within one half can have different colors, as long as it is clear to which half a cubie belongs.
If different cubie colors are not available, dot color can be used to indicate to which half a cubie belongs.
Dot counts above sixteen are hard to read and implement. Alphabets can be an option for lower counts above sixteen. For higher counts, regular numbers can be used, where two digit numbers allow designs up to 99 facelets. When using markings other than domino dots, the resulting puzzle should be called "Domino Style" instead of "Domino".
The following projects are documented in more detail here.
An explanation of the original Rubik's Domino, along with a brief description how to build one using current cuboids.
How to interpret the Domino Principle, and apply it to a 3×3×3 Cube.
How to apply the Domino Principle to a 4×4×4 Cube, including the 4×4×4 "Scarlet" Domino Cube.
Some lower order Twisty Puzzle Domino.
How to apply the Domino Principles to Stickerless Cubes.
How to apply the Domino Principles in Special Cases.
Summary of all finished Projects:
|Black 1×1×1||Classic||Black 1×1×1 Domino|
|Black 2×2×1 Floppy Cube||Classic||Black 2×2×1 Domino|
|Black 3×3×1 Super Floppy Cube||Classic||Black 3×3×1 Domino|
|White 3×3×1 Super Floppy Cube||Classic||White 3×3×1 Domino|
|Black + White 2×2×2 Cube||Classic||Leading Black 2×2×2 Domino + Leading White 2×2×2 Domino|
|Black + White 3×3×2 Cuboid||Classic||Leading Black 3×3×2 Domino + Leading White 3×3×2 Domino|
|Black + White + 2× Clear 3×3×3 Cube||Classic||Leading Black 3×3×3 Domino + Leading White 3×3×3 Domino|
|Black + White 4×4×4 Cube||Classic||Leading Black 4×4×4 Domino + Leading White 4×4×4 Domino|
|4×4×4 "Checker" Cube||Black+White, single color dots||Leading Black 4×4×4 "Scarlet" Domino|
|Stickerless 2×2×3 Cuboid||Color Cubies, single color dots||"Fire & Ice" 3×2×2 Domino|
|2× Stickerless 3×3×2 Cuboid||Color Cubies, single color opposite faces, single dot color||"Fire" 3×3×2 Domino + "Ice" 3×3×2 Domino|
|2× Stickerless 3×3×4 Cuboid||Color Cubies, single color opposite faces, single dot color||"Fire" 3×3×4 Domino + "Ice" 3×3×4 Domino|
|2× Stickerless 3×3×4 Cuboid||Color Cubies, six colors with four rings, single dot color||"Rainbow" 3×3×4 Domino, Leading yellow face + Leading white face|
|Black 5×5×4 Cuboid||Domino Style, Alphabet, Label Color||Black "Domino Style" Silver/Gold Alphabet Cuboid|
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