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Results tagged with convex-polytopes
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user 3568
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
4
votes
Accepted
Is the number of vertices of a convex $d-$dimensional lattice polytop without interior latti...
Encouraged by Andre Henriques' comment (and not seeing a response which puts more constraints on the problem), I shall promote my comment to an answer.
Consider an arbitrary convex polygon P in R^2 w …
- 1,036
7
votes
Accepted
Finding the convex combination of vertices which yields an inner point of a polytope
Hopefully I am using the right notion of convex combination. The following requires at most n+1 steps, however I do not know how complicated a step is.
Take the given point x and a vertex v visible …
- 1,036
0
votes
Vertex-transitive polytopes in any dimension with any number of vertices?
For v prime, I don't know. For v even, and d=3, one can take a regular polygonal prism. I can think of toriodal versions for odd composite v, but I am unsure they are vertex transitive. I can go to …
- 1,036