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Topic: Why two hypercubes can not be reassembled into a bigger hypercube
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Posts: 35
Registered: 12/4/04
Why two hypercubes can not be reassembled into a bigger hypercube
Posted: Jul 4, 2005 10:00 AM
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Refer to my message posted a few days ago. The same process applies to cubes in higher dimensions. The series generated by adding hypercublets layer by layer to a n^4 cube is given by the expression (n+k)^4-k^4. The starting points of each series is not a fourth power and, as the differences between the successive layers are the same as the differences between the series of fourth powers, another fourth power will never be 'hit'. The general formula for such a series is (n+k)^d - k^d where n is the size (number of cublets per side)of the original cube, k the number of layers and d the dimension of the cube.

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