Considering the figure in $R^3$ defined by:
$3-cosh(\sqrt{x^2+y^2})\geq{z}\geq{cosh(\sqrt{x^2+y^2})-1}$
I want to parametrize the surface of this body.
I have studied parametrizations of circles, torus, cones... However the figure that I am trying to parametrize now is hard to imagine and not intuitive. How can I parametrize it? Is there a general method to do it?