The Deltoidal Icositetrahedron is not an easy shape to make. It turns up in garnet and other small crystals for some reason. Also it has 26 variables (and corners), which makes it a little strange algebra wise in the English alphabet.
At a cubic locating resolution of 13^{3} as a minimum starting point, we find this geometry can be made. This it is its minimum resolution, meaning it likely has folding errors starting around n=3, deviating from the exact polynomials of (A+B+C+D+E+F+G+H+I+J+K+L+M+N+O+P+Q+R+S+T+U+V+W+X+Y+Z)^{n }Not that the coefficient numbers displayed at n=3 is visible enough for anyone to check and make sure this is true. Thee geometry is still n-based, starting at n=1. It is viewable here up to n=3. The mathematically correct (not just geometrically) has 175 dots at N=1, or 151 dots as a polarized structure, both performed amazingly at a resolution of 33^3. Check the Pascalloid Calculator program for that version.
For the mathematically correct version, there is both a combinatoric and algebreic solution.

26^{1} = 26

26^{2} = 676

26^{2} = 17,576