# Tagged Questions

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

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### construction of four dimensional regular convex polytopes

Could anybody give me a reference book about the explicit construction of the 6 regular four dimensional convex polytopes. I cannot easily find Schläfli's original paper so I am looking for a modern ...
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### An affine invariant of convex bodies

The following invariants of "pointed" convex bodies (i.e., pairs consisting of a convex body and a distinguished point in its interior) roughly measure how many of its linear images fit between the ...
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### The Stock Market Polytope: Explanation?

Ovidiu Racorean. "Crossing Stocks and the Positive Grassmannian I: The Geometry behind Stock Market." (arXiv Abstract link) Anyone care to offer a summary of what's going on here? (The ...
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### Study of convex polytopes via commutative algebra

Let $P \subset \mathbb{R}^d$ be any convex polytope with integral vertices, and let $M$ be the additive submonoid of $\mathbb{R}^{d+1}$ which is generated by $\{ (v,1) : v \in P \cap \mathbb{Z}^d \}$. ...
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### Normal polytopes - counterexample?

An integral polytope $P$ is normal if all lattice points inside the integer dilation $kP$ can be expressed as $p_1+p_2+\dots+p_k$, where $p_i \in P$ are lattice points. I am looking for an example $P$...
By lattice points, I will always mean points in $\mathbb{Z}^n$ and all polytopes here are convex rational polytopes. If $P$ is an integral polytope, the counting function for the number of lattice ...
I have a high-dimensional, non-empty polytope $Ax\geq b$ sitting inside the cube ($0\leq x_i \leq 1$). Is there any general theory or technique to show that this polytope contains an integer point, ...