I was hoping someone could help me determine explicitly the parameterized equations in 3D plane geometry (x,y,z) for a hyperbolic dodecahedron, and ideally the other hyperbolic form platonic solids Tetrahedron, Hexahedron [cube], and Icosahedron. I'm modeling them using MathMod and the programming language is in explicit parametric form. I'm not familiar with how to calculate the shapes in this way, but did find the hyperbolic octahedron in it's explicit parametric form, including it's intervals, using the mathworld-wolfram website [http://mathworld.wolfram.com/HyperbolicOctahedron.html], but the formulas weren't included in the other hyperbolic shapes.
How would I go about converting these shapes into this form?