The Dodecahedron seems like a terrible shape to make a Pascalloid out of, but it is required by Plato.

I found that the resolution of 17^{3} the shape is rather solvent, that likely has no folding errors until N=3 or 4 in terms of deviating from the exact polynomials of (A+B+C+D+E+F+G+H+I+J+K+L+M+P+Q+R+S+T+U+V)^{N}

The geometry is still n-based, starting here at N=1. It is viewable here up to N=3.

Anyway I don't know its Combinatoric Equation and I doubt it has one.

20^{1} = 20

20^{2} = 400

20^{3} = 8,000