Enumeration of integral tetrahedra

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(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 4x4 matrices with diameter d fulfilling the triangle inequalities we derive an exact formula.
Wir bestimmen die Anzahl ganzzahliger Tetraeder mit Durchmesser d bis auf Isomorphie für alle d kleiner gleich 1000. Der zugrunde liegende Algorithmus hat eine Zeitkomplexität von O(d^5) und basiert auf impliziter Erzeugung.

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Metadaten
Institutes:Mathematik
Author: Sascha Kurz
Year of Completion:2007
SWD-Keyword:Geometrische Kombinatorik; Geometrische Wahrscheinlichkeit; Tetraeder
Tag:ganzzahlige tetraeder; geometrische Wahrscheinlichkeit; ordnungstreues Erzeugen
Euclidean metric; canonicity check; geometric probability; implicit enumeration; integral tetrahedra; orderly generation
Dewey Decimal Classification:510 Mathematik
MSC-Classification:33F05 Numerical approximation and evaluation [See also 65D20]
URN:urn:nbn:de:bvb:703-opus-4275
Document Type:Working Paper
Language:English
Date of Publication (online):15.04.2008