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Non-Bandaged Siamese Cube
Above:Checkerboard Pattern
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Two 3x3x3's fused together to share not a single piece.

The Siamese Cubes is one of the oldest transformations. The first puzzle shared a block of size 1x1x3. Since 1980 all other possible sizes for shared blocks had been implemented.
Years later the inventor found one missing variant, with no shared cubies. The result consists of two unbandaged 3x3x3 joined by a bit of steel and some epoxy.

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