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five lines of symmetry :)
What is a nonagram? A nine pointed star, perhaps. In any case, a general nonagram, like a general (ie non regular) polygram(!) has NO lines of symmetry.
It can have as many lines of symmetry as it has points.
A regular six pointed star.
Assuming it is regular, there should be 6 lines of symmetry, three running from a tip to the tip opposite it, and three through the points that the tips meet.