An exact formula is given for the maximum number of edges in a graph that admits a three-dimensional grid-drawing contained in a given bounding box. The first universal lower bound on the volume of threedimensional grid-drawings is obtained as a corollary. Our results generalise to the setting of multi-dimensional polyline grid-drawings.

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Bose, P, Czyzowicz, J. (Jurek), Morin, P, & Wood, D. (2006). The maximum number of edges in a three-dimensional grid-drawing. doi:10.1142/9789812773289_0002