Let d be a metric on the n-D digital space Zn. The hypersphere Hd(r) of radius r, r integer, and center at origin is defined as Hd(r) equals {x : x (epsilon) Zn & d(x) ≤ r}. For example, Das and Chatterji studied the structure, volume and surface of such digital hyperspheres for the m-neighbor distance dnm. On generalization to dnm the N-sequence distance d(B) was proposed with the contention that these will define hyperoctagons in n-D. However, the hyperoctagonality of d(B)'s has not been established so far except for the special cases of 2- and 3-D and for dnm's in n- D. In this paper we explore the structure of the hyperspheres of d(B)'s in n-D to show that they truly are hyperoctagons. In particular we derive a formula to compute the corners of such hyperoctagons given a B and a r.
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