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Enumeration of Integral Tetrahedra
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Sascha Kurz

Department of Mathematics

Universität Bayreuth

D-95440 Bayreuth

Germany

**Abstract:**

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*(*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 4×4 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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