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See detailSlices, slabs, and sections of the unit hypercube
Marichal, Jean-Luc UL; Mossinghoff, Michael J.

in Online Journal of Analytic Combinatorics (2008), 3

Using combinatorial methods, we derive several formulas for the volume of convex bodies obtained by intersecting a unit hypercube with a half-space, or with a hyperplane of codimension 1, or with a flat ... [more ▼]

Using combinatorial methods, we derive several formulas for the volume of convex bodies obtained by intersecting a unit hypercube with a half-space, or with a hyperplane of codimension 1, or with a flat defined by two parallel hyperplanes. We also describe some of the history of these problems, dating to Pólya's Ph.D. thesis, and we discuss several applications of these formulas. [less ▲]

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