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We consider certain exponential box splines £ on a three-direction mesh whose exponents satisfy a symmetry condition. It is shown, in particular, that given bounded data on the integer lattice in R 2 , there is a unique bounded combination of integer translates of £ that interpolates the data. When all exponents are zero, this reduces to a result of de Boor, Hollig and Riemenschneider in  . Unlike the proof in  we use only elementary analysis and do not employ any computer calculations.doi:10.1017/s0013091500018174 fatcat:pmzmbbccjze5pjawqtuohkfvm4