I have this fan that I've been trying to construct a toric variety from. The problem is, it contains certain edges twice. These are the edges:
$$(1,0,1)$$ $$(0,1,1)$$ $$(-1,-1,1)$$ $$(0,0,1)$$ $$(0,0,1)$$
The last one appears "twice". Or at least that is what my calculation says. Without the double last entry, this would just be $\mathcal{O}(-3)$ over $\mathbb{CP}^2$.
I've been using the construction found in the Mirror Symmetry book by Hori et al. I have a matrix of charges $Q$
$$ Q^T = \begin{pmatrix} 1 & 1 & 1 & -3 & 0 \\ 1 & 1 & 1 & 0 & -3 \end{pmatrix} $$
Then the Edges $\Sigma(1)$ of the fan $\Sigma$ are given by the kernel of this matrix $Q$ as
$$ \sum_{i=1}^5 Q_{ia} v_i = 0$$
And I get the above edges.
I'm specifically interested in the Divisor corresponding to this last entry. So, what happens when I have an edge twice? Or is this not allowed?