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Results tagged with convex-polytopes
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user 32507
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
1
answer
158
views
Lifting of a spherical graph
Let us be given a topological graph $G$
on the unit sphere in $\mathbb{R}^3$
whose edges are minor arcs of great circles.
We suppose that the graph is $3$-vertex-connected
and that a pair of edges may …
- 1,724
2
votes
Accepted
A converse question about the polyhedrality under linear mapping
I think we can argue as in https://mathoverflow.net/a/423284/32507 to answer the question in the affirmative.
Let $\mathcal R_K(x)$ be the radial cone of $K$ at $x$ (as defined in the other answer). F …
- 1,724
0
votes
On faces of polytopes
The set $K_A$ is essentially a polar of $A$. Indeed, we have
$$
A = \{ x \in \mathbb R^n \mid l(x) \ge t \; \forall (l,t) \in K_A\} =: B.$$
The inclusion "$\subset$" is clear and in order to check "$\ …
- 1,724