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Betcha thought Rubik's Cube only went up to 5x5x5, didncha? Well, there's this company in Greece called V-Cube that makes 5x5x5, 6x6x6 and 7x7x7 cubes. The 7x7x7 cube has spherically curved faces because it would be geometrically impossible to make it with flat sides; there'd be no way to attach the corner pieces.
Left to right:
Eastsheen 2x2x2 (Eastsheen is a Chinese company that makes various cube-type puzzles. Damn, I bet that thing's chock fulla melamine...)
Rubik's Cube
Eastsheen 4x4x4
V-Cube 5
V-Cube 6
V-Cube 7
Doesn't it look like a filmstrip of a swirling cube vortex that's raging out of control and is about to explode? :}
Left to right:
Eastsheen 2x2x2 (Eastsheen is a Chinese company that makes various cube-type puzzles. Damn, I bet that thing's chock fulla melamine...)
Rubik's Cube
Eastsheen 4x4x4
V-Cube 5
V-Cube 6
V-Cube 7
Doesn't it look like a filmstrip of a swirling cube vortex that's raging out of control and is about to explode? :}
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Imagine a cube sliced into 7 equal layers along all 3 axes, making a 7x7x7 array of cubelets.
Now imagine rotating one of the outermost layers 45 degrees.
The corner cubelet will completely clear the edge of the next layer.
Now imagine rotating it back and doing the same for the other two faces that that corner cubelet is a part of. It will completely clear the rest of the cube on all 3 sides, which means there's no way to attach it to the internal mechanism of the cube, and it would fall off.
The pillowed shape of the V-Cube 7 prevents this by bowing up the sides and permitting the corner cubes to stay in contact with the cube's interior throughout the turn.
If the sides were flat, the corner pieces would fall out.
Somewhere around I have a Rubik's Cylinder, which I admit is probably more closely related to one of those sliding tile puzzles (2 of one color, 3 each of the other colors, line each color up in rows), except I hate those sliding-tile puzzles but like the rubik's cylinder thing.
The Eastsheen and V-Cube puzzles are available in black or white plastic, whereas Rubik's only uses black plastic.