# Polytope

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• Mar 23rd 2013, 04:27 PM
sunmalus
Polytope
Hi, I need help with this:
Let P be a non-empty polytope.
I) Prove that P has vertices.
II)Let $u_1, \dots u_l \in \mathbb{R}^n$ be the vectrices of P. Show that $P=conv(\{u_1, \dots u_l \}).$

for the first one I see why P has vertices, if P is bounded and $P=\{ x \colon Ax\leq b \}$ then if $x \in P$, x is also bounded so A must be full colon rank. But this is just an idea and I'm not even sure it's correct.

if you can just give me a hit for II) it would be great.

Thanks in advance!
• Mar 23rd 2013, 05:20 PM
chiro
Re: Polytope
Hey sunmalus.

For those who are not familiar with polytypes (like myself), what is the structure of a polytype (like the set structure)?