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When 3 cubes interpentrate in an optimal way they create dozens of smaller closed bounded volumes ... like M. C. Escher's Waterfall picture with the cube-3 compound. For Escher's 3 interpenetrating cube figure, what is the count of all the interior and exterior closed bounded volumes? Are there any references to an answer to this?


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A link to the picture would help. – Christian Blatter Mar 5 '12 at 16:18

In your link to MathWorld it says. 'The Escher compound divides the three component cubes into 67 individual cells (Hoeflin 1985). '

The answer can be obtained by counting.

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And if you want to count "all space outside the cubes" as another cell, you would get 68 individual cells. (At least that's my interpretation of the MathWorld link, and it looks right to me. I didn't actually count them.) – Jonas Kibelbek Mar 6 '12 at 20:19

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