## Strugles with VERTICES_IN_FACETS

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Joined: 06 Feb 2019, 16:59

### Strugles with VERTICES_IN_FACETS

Hello,
I am a new user on polymake and need some help.
Here is my problem:
My purpose is to compute a cone $c pointed at some vertex$v of a polytope $p, such that its rays are the affine hull of the facets of$p incident to $v, and such that$p itself is not contained in $c. So my question is: how can I keep track of the facets that are incident to my vertex$v, meaning to get their inequalities and affine hull. VERTICES_IN_FACETS and FACETS_THRU_VERTICES only seems to show the labels of the vertices and facets not information on them. Or am I wrong?

Thank you very much, and apologies for my english.

joswig
Main Author
Posts: 216
Joined: 24 Dec 2010, 11:10

### Re: Strugles with VERTICES_IN_FACETS

My purpose is to compute a cone $c pointed at some vertex$v of a polytope $p, such that its rays are the affine hull of the facets of$p incident to $v, and such that$p itself is not contained in $c. Sorry, I do not understand what you want to compute. Do you want to compute the intersection of the affine halfspaces given by the facets through a fixed vertex? This would be like the following. Code: Select all >$c=cube(3); > print $c->VERTICES->[0]; 1 -1 -1 -1  Just to check which vertex is indexed with 0. Here you see the indices of the facets containing that vertices (as row indices to the FACETS matrix). Code: Select all > print$c->FACETS_THRU_VERTICES->[0]; {0 2 4} 
If you want to get the inequalities:

Code: Select all

> print $c->FACETS->minor($c->FACETS_THRU_VERTICES->[0],All); 1 1 0 0 1 0 1 0 1 0 0 1 
And you can produce a new object of type Polytope, of course:

Code: Select all