So basically the representatives of the Void is velkoz
http://universe.leagueoflegends.com/en_AU/region/void
It seems the symbol is made with three arms and eyes. Is it because his species are the only one with sentience?
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Every type we've seen fits that bill, except for Rek'Sai. Odds are his kind is the only one able to overcome their constant need to devour in order to do other things.
Vel'koz is definetly not the only one with sentience,I mean there is a reason why 
and even 
can talk(cho'gath is even said to be quite intelligent in his lore)
And I guess it is simply a coincidence.
I mean search for "void symbol" and you'll get tons of swirly symbols to represent the element of void. They likely chose 3 lines,because 4 would have looked like a swastika,2 would have been too few and 5 would have been too crowded. The circles were likely added to make the symbol not too plain.