How to find the coordinates of a regular polyhedron We well know that to find the coordinates of the vertices a polygon, we can simply solve the complex variable equation $z^n-1=0$ (and scale them as we wish).
Is there an analog method to find the coordinates of the vertices of a Platonic solid? 
For example something like solving an equation such as $(x^2+y^2+z^2)^{n/2}-1 = 0$, for certain numbers $(x,y,z)$? and if so, how to solve this?
Thanks.
H.

When in doubt,  google.
https://en.wikipedia.org/wiki/Platonic_solid#Cartesian_coordinates
It's not a general formula but simply a statement of the 5 cases with graphical explanations why.
