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Results tagged with convex-polytopes
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user 56391
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
8
votes
1
answer
328
views
Monge-Ampère measures and Kazarnovskii pseudovolume
Let $\Gamma\subset\mathbb C^n$ be a convex polytope and let $h_\Gamma(z)=\max_{v\in\Gamma}{\rm Re}\langle z,v\rangle$ be its support function with respect to the standard scalar product on $\mathbb C^ …
CommunityBot
- 1
1
vote
Monge-Ampère measures and Kazarnovskii pseudovolume
I finally found a purely current theoretical proof of the equality
\begin{equation*}
\mu_1(B_{2n})
=
2^{n-1}(n-1)!
\sum_{\Delta\in{\mathcal B}(\Gamma,1)}
{\mathop{\rm vol\,}\nolimits}_{1}(\Delta)
{\ma …
- 311
4
votes
0
answers
363
views
On intrinsic volumes
Let $\Gamma$ be a convex polytope in $\mathbb R^n$. The $k$-th intrinsic volume of $\Gamma$ is the number
$$
\text{v}_k(\Gamma)=\sum_{\Delta\in{\mathcal B}(\Gamma,k)}\text{vol}_k(\Delta)\psi_\Gamma(\D …
- 311
0
votes
0
answers
66
views
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 r …
- 311