Journal of Integer Sequences, Vol. 10 (2007), Article 07.9.3

Enumeration of Integral Tetrahedra

Sascha Kurz
Department of Mathematics
Universität Bayreuth
D-95440 Bayreuth


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.

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(Concerned with sequences A000041 A000065 and A002620 .)

Received June 18 2007; revised version received September 3 2007. Published in Journal of Integer Sequences, September 3 2007.

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