  We determine the numbers of integral tetrahedra with diameter $d$ up to
isomorphism for all $d\le 1000$ via computer enumeration. Therefore 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.
