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.
