  For any symmetry group $H$ and any appropriate matrix dilation we give an
explicit method for the construction of $H$-symmetric refinable interpolatory
refinable masks which satisfy sum rule of arbitrary order $n$. For each such
mask we give an explicit technique for the construction of dual wavelet frames
such that the corresponding wavelet masks are mutually symmetric and have the
vanishing moments up to the order n. For an abelian symmetry group $H$ we
modify the technique such that each constructed wavelet mask is $H$-symmetric.
