The formula for the j-function which employs polynomial invariants of the icosahedron,
$$j(\tau)=-\frac{(r^{20} - 228r^{15} + 494r^{10} + 228r^5 + 1)^3}{r^5(r^{10} + 11r^5 - 1)^5}$$
where,
$$r^{-1}-r=\frac{\eta{(\tau/5)}}{\eta{(5\tau)}}+1$$
and $r = r(\tau)$ is the Rogers-Ramanujan continued fraction and the modular form Dedekind eta function $\eta{(\tau)}$ is well-known.
Question: Is there a similar relationship between any of the six regular 4D polytopes and some known modular form?
P.S. Somebody asked me this question.