Summary: We determine the number of integral tetrahedra with diameter $d$, up to isomorphism, for all $d \le 1000$, via computer enumeration. We give an algorithm that enumerates the integral tetrahedra with diameter at most $d$ in $O(d^{5})$ time and an algorithm that can check the canonicity of a given integral tetrahedron with at most 6 integer comparisons. For the number of isomorphism classes of integral $4\times 4$ matrices with diameter $d$ fulfilling the triangle inequalities we derive an exact formula.

33F05, 05A15

implicit enumeration, integral tetrahedra, geometric probability, Euclidean metric, orderly generation, canonicity check