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### Polyhedra, facets and vertices

I have a 6 dimensional, convex, compact polyhedron in R^12, that I am calling P1. The polyhedron P1 was specified by giving a large number of inequalities. When I enter P1.faces(5) into sage, I get the following

(A 5-dimensional face of a Polyhedron in RDF^12 defined as the convex hull of 6 vertices,

A 5-dimensional face of a Polyhedron in RDF^12 defined as the convex hull of 7 vertices,

A 5-dimensional face of a Polyhedron in RDF^12 defined as the convex hull of 7 vertices,

A 6-dimensional face of a Polyhedron in RDF^12 defined as the convex hull of 7 vertices,

A 5-dimensional face of a Polyhedron in RDF^12 defined as the convex hull of 6 vertices,

A 6-dimensional face of a Polyhedron in RDF^12 defined as the convex hull of 8 vertices,

etc. How can there be two 6-dimensional faces, each with a different number of vertices, on the boundary of P1? I have checked that P1 really does have dimension 6.

Also, when I try to find a list of vertices on the boundary of any 5-dimensional face of P1, for example P1.faces(5)[0].vertices_list() I get an error message

AttributeError: 'tuple' object has no attribute 'vertices_list'

However, P1.faces(5)[0].vertices() works. My second question is, how do I get a list of vertices on the boundary of an n dimensional face?

Thanks a lot!

 2 None slelievre 15189 ●16 ●140 ●302 http://carva.org/samue...

### Polyhedra, facets and vertices

I have a 6 dimensional, 6-dimensional, convex, compact polyhedron in R^12, $\mathbb{R}^{12}$, that I am calling P1. P1. The polyhedron P1 P1 was specified by giving a large number of inequalities. When I enter P1.faces(5) P1.faces(5) into sage, Sage, I get the following

(A 5-dimensional face of a Polyhedron in RDF^12 defined as the convex hull of 6 vertices, vertices,
A 5-dimensional face of a Polyhedron in RDF^12 defined as the convex hull of 7 vertices, vertices,
A 5-dimensional face of a Polyhedron in RDF^12 defined as the convex hull of 7 vertices, vertices,
A 6-dimensional face of a Polyhedron in RDF^12 defined as the convex hull of 7 vertices, vertices,
A 5-dimensional face of a Polyhedron in RDF^12 defined as the convex hull of 6 vertices, vertices,
A 6-dimensional face of a Polyhedron in RDF^12 defined as the convex hull of 8 vertices, etc.
vertices,
...)


How can there be two 6-dimensional faces, each with a different number of vertices, vertices, on the boundary of P1? P1? I have checked that P1 P1 really does have dimension 6.

Also, when I try to find a list of vertices on the boundary of any 5-dimensional face of P1, P1, for example P1.faces(5)[0].vertices_list() example

P1.faces(5)[0].vertices_list()


I get an error message

AttributeError: 'tuple' object has no attribute 'vertices_list''vertices_list'


However, P1.faces(5)[0].vertices() works. P1.faces(5)[0].vertices() works.

My second question is, how do I get a list of vertices on the boundary of an n dimensional $n$-dimensional face?

Thanks a lot!