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 (email@example.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.