2x2x2x2, part 6

Now that you’ve seen what it looks like to rotate a 2×2 block inside a three dimensional cube, let’s see what happens when we rotate a 2×2 block inside a four dimensional hypercube. It turns out that there are at least six different ways you can rotate the same 2×2 block within a 2x2x2x2 hypercube:


0 1
2 3


4 5
6 7


8 9
a b


c d
e f


0 1
2 3


4 5
6 7


8 9
a b


c d
e f


0 1
2 3


4 5
6 7


8 9
a b


c d
e f


0 1
2 3


4 5
6 7


8 9
a b


c d
e f


0 1
2 3


4 5
6 7


8 9
a b


c d
e f


0 1
2 3


4 5
6 7


8 9
a b


c d
e f

All six of the above cases represent the same 2×2 shape embedded in a 2x2x2x2 hypercube. The only difference is how they are rotated differently (in four dimensions, of course). The good news is that all those rotations provide lots of opportunities to make really interesting puzzles.

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