On Indecomposable Polyhedra and the Number of Steiner Points

dc.bibliographicCitation.firstPage343eng
dc.bibliographicCitation.journalTitleProcedia engineeringeng
dc.bibliographicCitation.lastPage355eng
dc.bibliographicCitation.volume124eng
dc.contributor.authorGoerigk, Nadja
dc.contributor.authorSi, Hang
dc.date.accessioned2022-07-06T06:08:34Z
dc.date.available2022-07-06T06:08:34Z
dc.date.issued2015
dc.description.abstractThe existence of indecomposable polyhedra, that is, the interior of every such polyhedron cannot be decomposed into a set of tetrahedra whose vertices are all of the given polyhedron, is well-known. However, the geometry and combinatorial structure of such polyhedra are much less studied. In this article, we investigate the structure of some well-known examples, the so-called Schönhardt polyhedron [10] and the Bagemihl's generalization of it [1], which will be called Bagemihl's polyhedra. We provide a construction of an additional point, so-called Steiner point, which can be used to decompose the Schönhardt and the Bagemihl's polyhedra. We then provide a construction of a larger class of three-dimensional indecomposable polyhedra which often appear in grid generation problems. We show that such polyhedra have the same combinatorial structure as the Schönhardt's and Bagemihl's polyhedra, but they may need more than one Steiner point to be decomposed. Given such a polyhedron with n ≥ 6 vertices, we show that it can be decomposed by adding at most interior Steiner points. We also show that this number is optimal in theworst case.eng
dc.description.versionpublishedVersioneng
dc.identifier.urihttps://oa.tib.eu/renate/handle/123456789/9630
dc.identifier.urihttps://doi.org/10.34657/8668
dc.language.isoengeng
dc.publisherAmsterdam [u.a.] : Elseviereng
dc.relation.doihttps://doi.org/10.1016/j.proeng.2015.10.144
dc.relation.essn1877-7058
dc.rights.licenseCC BY-NC-ND 4.0 Unportedeng
dc.rights.urihttps://creativecommons.org/licenses/by-nc-nd/4.0/eng
dc.subject.ddc670eng
dc.subject.gndKonferenzschriftger
dc.subject.otherBagemihl's polyhedroneng
dc.subject.otherIndecomposable polyhedroneng
dc.subject.otherSchönhardt polyhedroneng
dc.subject.otherSteiner pointeng
dc.subject.othertetrahedralizationeng
dc.titleOn Indecomposable Polyhedra and the Number of Steiner Pointseng
dc.typeArticleeng
dc.typeTexteng
dcterms.event24th International Meshing Roundtable (IMR 2015), 12-14 October 2015, Austin, Texas, USA
tib.accessRightsopenAccesseng
wgl.contributorWIASeng
wgl.subjectIngenieurwissenschafteneng
wgl.typeZeitschriftenartikeleng
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