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Rodrigo de Azevedo
Rodrigo de Azevedo
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Fix $m,n\in\mathbb{N}$$m,n \in \mathbb{N}$ with $m\ge n+1$$m \ge n+1$. Take $m$ points in general position in $\mathbb{R}^n$ and let $P$ be their convex hull. What is the maximal number of (external, codimension-one) faces that $P$ can have, in terms of $m$ and $n$? (Apologies if this is a well-known quantity.)

(Apologies if this is a well-known quantity.)

Fix $m,n\in\mathbb{N}$ with $m\ge n+1$. Take $m$ points in general position in $\mathbb{R}^n$ and let $P$ be their convex hull. What is the maximal number of (external, codimension-one) faces that $P$ can have, in terms of $m$ and $n$? (Apologies if this is a well-known quantity.)

Fix $m,n \in \mathbb{N}$ with $m \ge n+1$. Take $m$ points in general position in $\mathbb{R}^n$ and let $P$ be their convex hull. What is the maximal number of (external, codimension-one) faces that $P$ can have, in terms of $m$ and $n$?

(Apologies if this is a well-known quantity.)

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zjs
zjs
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Polytope with most faces

Fix $m,n\in\mathbb{N}$ with $m\ge n+1$. Take $m$ points in general position in $\mathbb{R}^n$ and let $P$ be their convex hull. What is the maximal number of (external, codimension-one) faces that $P$ can have, in terms of $m$ and $n$? (Apologies if this is a well-known quantity.)