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Results tagged with convex-polytopes
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user 4213
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
14
votes
coordinates of vertices of regular simplex
One interesting problem is to determine the $n$ such that there is
a regular simplex in $\mathbb{R}^n$ with rational/integer coordinates.
This is a well-known old problem which I discussed in
this 199 …
- 20.8k
12
votes
Accepted
Ehrhart polynomial
If you mean the polytope with vertices $(0,\ldots,0,\pm1,0,\ldots,0)$
then it is easily seen to be
$$\sum_{k=0}^d 2^k{d\choose k}{x\choose k}.$$
- 20.8k