On Smith normal forms of q-Varchenko matrices

In this paper, we investigate $q$-Varchenko matrices for some hyperplane arrangements with symmetry in two and three dimensions, prove that they have a Smith normal form over $\mathbb Z[q]$. particular, examine the arrangement regular $n$-gon plane dihedral model space Platonic polyhedra. each case, matrix associated has Z[q]$ realize their congruent transformation as well.