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We analyze the approximation and smoothness properties of quincunx fundamental re nable functions. In particular, we provide a general way for the construction of quincunx interpolatory re nement masks associated with the quincunx lattice in R 2 . Their corresponding quincunx fundamental re nable functions attain the optimal approximation order and smoothness order. In addition, these examples are minimally supported with symmetry. For two special families of such quincunx interpolatory masks,doi:10.1090/s0025-5718-00-01300-4 fatcat:5xou5g3yirhstdeenqr36irale