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What are the general techniques for proving a variety is not toric?

When I read the paper "A survey on Cox rings" with the link below:

http://math.berkeley.edu/~velasco/Survey.pdf

In Section 4.2 it is mentioned that the Del Pezzo surface given by blowup of $\mathbb{P}^2$ at $s>3$ general points is not toric. Is there an easy way to see this?

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