Plane figures have their equations. I found their expressions
in which the absolute function |x| is used, or which converge
into their corresponding shapes respectively as the value of
included parameter approaches infinity.
In the case that the number of vertexes is even number, a general
equation for 2 m-gon which does not contain |x| or " 
" calculations
is found.
Since you can easily confirm,
by several kinds of plotting tool, that the expressions are correct,
I do not give you how to derive them. If you need the derivations
of the equations, e-mail me (yoshi.tamori@gmail.com).
In the case of odd number vertexes, I do not know a general answer. The general equations should be simpler. However, the results are not be applicable for numerical calculations, since the infinity precision is required to calculate the location of each vertex.