If the use of the absolute function |x| was allowed, it is possible that we give a equation for n-gon by
where the is a periodic function in the period which is defined in the domain (Note thus .) Though I hope to have simpler expression than this, this is the simplest expression so far that I can give you. This expression gives you a n-gon under the ideal precision of calculation, since the infinite precision would be required for the calculations at the vertexes.