This reminds me of a definition of dimension - that dim n is such that a
maximum of n+1 measure polytopes can meet at a single vertex with dim n
overlaps. In 2d, 3 squares meet in a 'brick' fashion; in 3d, 4 cubes meet
with 4 planes touching (think brick fashion flat, with a 4th brick on top,
overlapping the point where the 3 meet), etc. So if you're caught in a
dimension you can't identify, build up with measure polytopes this way,
and subtract 1... - Alan
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