Simple Partitions of Space
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Consider an arrangement of n planes in general position in Euclidean 3-space, where by "general position" we mean that at most three of the planes pass through each point, no more than two of the planes pass through each line, there are no parallel planes, and no lines of intersection are parallel to planes of the arrangement. Into how many cells is space divided? This problem is studied from the heuristic point of view by G. P6lya in [4] and again in his film, "Let Us Teach Guessing." The solution,
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[3] George Polya,et al. Induction and Analogy in Mathematics , 1954 .
[4] T. Zaslavsky. A combinatorial analysis of topological dissections , 1977 .