Enumeration of integral tetrahedra

Abstract

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.

10 pages, 1 figure

Cited by in corpus (1)

• On the minimum diameter of plane integral point sets