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Results tagged with convex-polytopes
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user 5371
Convex polytopes are the convex hulls of a finite set of points in Euclidean spaces. They have rich combinatorial, arithmetic, and metrical theory, and are related to toric varieties and to linear programming
7
votes
Area of cross-section (at midpoint perpendicular to longest diagonal) in the unit cube of di...
This is a very old problem and there is a classical analytic approach to it. You can express the volume of sections of a convex body in terms of the Fourier transform of powers of the Minkowski functi …
- 22.3k
4
votes
Accepted
A variation on "Hearing the shape of a drum" for polytopes.
The short answer is that there are no particular constraints on the spectral decomposition of the function $\varphi$, as long as a basic convexity condition is satisfied.
Lemma..Assume that $\var …
- 22.3k
18
votes
Accepted
On the number of Archimedean solids
A proof of the enumeration theorem for the Archimedean solids (which basically dates back to Kepler) can be found in the beautiful book "Polyhedra" by P.R. Cromwell (Cambridge University Press 1997, p …
- 22.3k