Lattice Cubes
Richard Parris · College Mathematics Journal · 2011
SummaryGiven a segment that joins two lattice points in R3, when is it possible to form a lattice cube that uses this segment as one of its twelve edges? A necessary and sufficient condition is that the length of the segment be an integer. This paper presents an algorithm for finding such a cube when the prime factors of the length are known, and shows that the cube is essentially unique if the given segment does not contain another lattice point.