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Results tagged with convex-polytopes
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user 2294
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
10
votes
Accepted
How many non-equivalent sections of a regular 7-simplex?
Here's the answer. The main claims (Claims 1-4) I am fairly sure I got right, but I could easily have missed a case (or counted an extra case) in the later enumeration. If anybody finds a mistake, ple …
6
votes
Minimal combinatorial data needed to define a polytope
In fact, elaborating on Guillermo Pineda-Villavicencio's answer, Jürgen Richter-Gebert's universality theorem for 4-polytopes shows that even in four dimensions, deciding whether a graph is realized b …
- 6,342
13
votes
Accepted
Is a given point in the interior of the convex hull of a given finite collection of points?
Take your linear program and add the objective function max $x$, and the inequalities $\lambda_i - x \geq 0$. If the point is on the exterior, the optimum solution has $x=0$. Otherwise, there is a sol …
- 6,342