Enumeration of integral tetrahedra

Details Enumeration of integral tetrahedra Enumeration of integral tetrahedra

2008-04-08

arxiv.org/abs/0804.1310v1

Mathematics

Combinatorics

10 pages, 1 figure

Scientific paper

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.

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