Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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?

http://mathworld.wolfram.com/Cube3-Compound.html

Ron

share|improve this question
    
A link to the picture would help. –  Christian Blatter Mar 5 '12 at 16:18

1 Answer 1

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.

share|improve this answer
1  
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

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.