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Results tagged with convex-geometry
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user 39521
A branch of geometry dealing with convex sets and functions. Polytopes, convex bodies, discrete geometry, linear programming, antimatroids, ...
5
votes
Accepted
Edges of the contact polytope of the Leech lattice
Using the unimodular scaling of the Leech lattice, the length of each minimal vector is $\sqrt{4}$. Fixing a particular minimal vector $u$, the remaining minimal vectors $v$ are:
1 vector $v$ with $\ …
- 12.4k
8
votes
Accepted
Is a polytope that has in-spheres for faces of all dimensions already regular?
This is true in all dimensions, and can be proved by induction (on $d$) applied to the following (slightly stronger) hypothesis:
Theorem: If $P$ is a convex $d$-polytope with $k$-in-spheres for all $ …
- 12.4k