Enumeration of integral tetrahedra

2008/04/08 by Sascha Kurz, Kurz, Sascha
Mathematics · #05A15 #33F05 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05A15 #msc:33F05

paper · pdf · doi:10.48550/arxiv.0804.1310

10 pages, 1 figure

arxiv created 2008/04/08 · arxiv updated 2009/12/01

Abstract

We determine the numbers of integral tetrahedra with diameter d up to isomorphism for all d≤ 1000 via computer enumeration. Therefore 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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