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Results tagged with convex-polytopes
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user 2672
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
1
vote
Combinatorial distance ≡ Euclidean distance
Thanks for the responses. They give many valuable hints.
Anyway: Does property X seem to be an interesting property or is it "just so"?
At first glance it looks like a fundamental property - similar …
- 9,720
1
vote
Combinatorial distance ≡ Euclidean distance
I wonder if the class of polytopes I am going to define might have property X:
Consider the regular n-simplex $\Delta^n$.
Let $F_k^n$ be the set of k-dimensional faces of $\Delta^n$:
$F_0^n$ = the …
- 9,720
8
votes
6
answers
1k
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Combinatorial distance ≡ Euclidean distance
Definition: A polytope has property X iff there is a function f:N+ → R+ such that for each pair of vertices vi, vj the following holds:
disteuclidean(vi, vj) = f(distcombinatorial(vi, vj))
with dist …
- 9,720
22
votes
4
answers
3k
views
Can you determine whether a graph is the 1-skeleton of a polytope?
How do I test whether a given undirected graph is the 1-skeleton of a polytope?
How can I tell the dimension of a given 1-skeleton?
- 9,720