# Questions tagged [polyhedra]

For questions on the set of points that satisfy a finite set of linear inequalities.

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### Faces and Facets in a convex polyhedron

I am willing to find the number of faces and facets in a convex polyhedron. Suppose, in the cube polyhedron there exists $8$ vertices, $12$ edges, and $6$ faces. It satisfies the Euler equation as ...
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### On the non-sufficiency of total unimodularity of the constraint matrix in the definition of an integer polytope

Is there an example of an $m\times n$ integer matrix $A$ and an integer vector $b\in \mathbb {Z}^{m}$ such that the polyhedron $P := \{ x\in \mathbb {R}^{n} \mid A x \leq b\}$ is integer, while $A$ is ...
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### Extreme rays of a small polyhedral cone: How do I get them?

In a nutshell I have a small 2-dimensional polyhedral cone. $$C=\{(x_1,x_2): 2x_1-x_2 \leq 0, x_1+3x_2 \leq 0\}$$ I am looking for a simple, illustrative, procedure to get its extreme rays. Any ...