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**skystar** in a pentagon, there are 10 symmetries ,5 rotational ,5 reflections, this question has baffled me for a while: from 2 symmetries (a generating set) every other symmetry can be described as a combination of these 2 symmetries but whenever i work out the other symmetries using the generating set it takes me forever using trial and error mucking about with composite functions are there laws as to generate the other symmetries,

i know a rotation can be expressed as reflection o reflection for example. but i find it very annoying not knowing. il try be more specific if this question is bit vague,tho ive done my best.thanks