In two dimensions, a lattice polygon is a polygon in a Cartesian coordinate plane such that the two coordinates of each vertex are integers. In three dimensions, a lattice polyhedron is a polyhedron such that the three coordinates of each vertex are integers.
(a) Prove that a lattice triangle cannot be an equilateral triangle.
(b) Is it possible for a lattice tetrahedron to be a regular tetrahedron?
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