Enumeration of Integral Tetrahedra
Department of Mathematics
We determine the number
of integral tetrahedra with diameter d, up to isomorphism,
for all d ≤ 1000, via computer enumeration.
We give an algorithm that enumerates the
integral tetrahedra with diameter at most d in
O(d5) 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 4×4 matrices with diameter d
fulfilling the triangle inequalities we derive an exact formula.
Full version: pdf,
(Concerned with sequences
Received June 18 2007;
revised version received September 3 2007.
Published in Journal of Integer Sequences, September 3 2007.
Journal of Integer Sequences home page