The Icosahedron is a little more fitting for a Pascalloid structure, but the resolution is heavy.

I found that the resolution of 21^{3} the shape is rather solvent, that likely has no folding errors until N=4 or 5 in terms of deviating from the exact polynomials of (A+B+C+D+E+F+G+H+I+J+K+L)^{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 either and I doubt it has one.

12^{1} = 12

12^{2} = 144

12^{3} = 1,728