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Definitions of 3-D digital surface and plane are introduced. Many geometric properties of these objects are examined. In particular, it is shown that digital convexity is neither a necessary nor a sufficient condition for a digital surface element to be a convex digital plane element, but it is both necessary and sufficient for a digital surface to be a digital plane. Also algorithms are presented to determine whether or not a finite set of digital points is a (convex) digital plane element.