# Think 2-D Is Cool? Wait Till You Try 3-D!

Geometry Level 3

A lattice cube is a cube in 3-dimensional space, whose vertices are lattice points. Describe the set of possible side lengths of a lattice cube.

Note: A lattice point is a point whose coordinates are all integers. $$(0,0,1)$$ is a lattice point, but $$(\frac{1}{2}, \sqrt{2}, -0.2 )$$ is not a lattice point.

For similar problems, you can read my note on Construction.

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