# 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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### reference for the cubical structure of the associahedra

I cannot find where I learned that the $n$-dimensional associahedron is a union of $n$-cubes. The vertices of the $n$-dimensional associahedron are the finite binary trees having $n+2$ leaves and ...
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### Inequality of arithmetic and geometric means for the lattice polytopes?

Let $K$,$L$,$M$ be convex lattice polytopes (so their vertices are in $\mathbb{Z}^n$) in $\mathbb{R}^n$ satisfying $K+L\subseteq M+M$ (Minkowski sum). Do we always have ...
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### Triangulations of polytopes and tilings of zonotopes

Consider a set $A = \{ a_1,a_2,\ldots, a_n \}$ of vectors in $\mathbb{R}^d$, which lie in a common affine hyperplane. Two convex polytopes may be obtained from $A$, namely the convex hull of the ...
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### Detecting tilings by toric geometry

This is probably a silly question, but I figured that if there is a good answer, this would be a good place to ask. Ever since I got my hands on the book "Toric Varieties" by Cox, Little and Schenck, ...
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### The facial structure of the convex hull of a family of characteristic functions

Let $S$ be a finite set and let $\mathcal{A} \subset\mathcal{P}(S)$ be a family of subsets of $S$. Consider the convex polytope spanned by the characteristic functions of members of $\mathcal{A}$ : ...
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### centrally symmetric neighborly polytopes.

Let $P$ is centrally symmetric $k$ neighborly d-polytope. Let $P^*$ is polar( also dual) of $P$. Consider a polytope $Q^*$ , $Q^* \subset P^*$( not necessarily a face of $P^*$). By duality ...