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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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How to know if convex-hull of a set contains zero?

Let $(\lambda_1 , \cdots , \lambda_d) \vdash k$ be a partition of $k$ of length $d$. Is there any way to decide if $0 \in \text{Conv}\{(\underbrace{\alpha_1, \cdots, \alpha_1}_{\lambda_1}, \cdots , \u …
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