Your simplex is not a full-dimensional simplex, so its a bit of a question 
of definition. We could

a) keep the "False" output but fix the docstring of is_simplicial to 
require full dimensionality, or

b) extend simplicial-ness to general polyhedra. Then they obviously aren't 
the duals of simple polytopes any more.

Preferences?



On Tuesday, August 11, 2015 at 4:38:26 PM UTC+2, Thomas Kahle wrote:
>
> Hi,
>
> I've stumbled upon the following polyhedron on which sage gives 
> contradictory answers.  This is sage-6.8.  Is this a bug?
>
> sage: Pw
> A 7-dimensional polyhedron in QQ^16 defined as the convex hull of 8 
> vertices
>
> sage: Pw.vertices()
> (A vertex at (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0),
>  A vertex at (1/3, 0, 0, 1/3, 0, 0, 0, 0, 0, 0, 0, 0, 1/3, 0, 0, 1/3),
>  A vertex at (1/3, 0, 1/3, 0, 0, 0, 0, 0, 1/3, 0, 1/3, 0, 0, 0, 0, 0),
>  A vertex at (1/9, 0, 1/9, 1/9, 0, 0, 0, 0, 1/9, 0, 1/9, 1/9, 1/9, 0, 1/9, 
> 1/9),
>  A vertex at (1/3, 1/3, 0, 0, 1/3, 1/3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0),
>  A vertex at (1/9, 1/9, 0, 1/9, 1/9, 1/9, 0, 1/9, 0, 0, 0, 0, 1/9, 1/9, 0, 
> 1/9),
>  A vertex at (1/9, 1/9, 1/9, 0, 1/9, 1/9, 1/9, 0, 1/9, 1/9, 1/9, 0, 0, 0, 
> 0, 0),
>  A vertex at (1/27, 1/27, 1/27, 1/27, 1/27, 1/27, 1/27, 1/27, 1/27, 1/27, 
> 1/27, 1/27, 1/27, 1/27, 1/27, 1/27))
>
> sage: Pw.is_simplex()
> True
> sage: Pw.is_simplicial()
> False
>
> Of course the last should come out "True"
>
> Cheers,
> Thomas
>

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