On decomposition of embedded prismatoids in $R^3$ without additional points
dc.bibliographicCitation.seriesTitle | WIAS Preprints | eng |
dc.bibliographicCitation.volume | 2602 | |
dc.contributor.author | Si, Hang | |
dc.date.accessioned | 2022-06-23T14:30:44Z | |
dc.date.available | 2022-06-23T14:30:44Z | |
dc.date.issued | 2019 | |
dc.description.abstract | This paper considers three-dimensional prismatoids which can be embedded in ℝ³ A subclass of this family are twisted prisms, which includes the family of non-triangulable Scönhardt polyhedra [12, 10]. We call a prismatoid decomposable if it can be cut into two smaller prismatoids (which have smaller volumes) without using additional points. Otherwise it is indecomposable. The indecomposable property implies the non-triangulable property of a prismatoid but not vice versa. In this paper we prove two basic facts about the decomposability of embedded prismatoid in ℝ³ with convex bases. Let P be such a prismatoid, call an edge interior edge of P if its both endpoints are vertices of P and its interior lies inside P. Our first result is a condition to characterise indecomposable twisted prisms. It states that a twisted prism is indecomposable without additional points if and only if it allows no interior edge. Our second result shows that any embedded prismatoid in ℝ³ with convex base polygons can be decomposed into the union of two sets (one of them may be empty): a set of tetrahedra and a set of indecomposable twisted prisms, such that all elements in these two sets have disjoint interiors. | eng |
dc.description.version | publishedVersion | eng |
dc.identifier.uri | https://oa.tib.eu/renate/handle/123456789/9186 | |
dc.identifier.uri | https://doi.org/10.34657/8224 | |
dc.language.iso | eng | |
dc.publisher | Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik | |
dc.relation.doi | https://doi.org/10.20347/WIAS.PREPRINT.2602 | |
dc.relation.issn | 2198-5855 | |
dc.rights.license | This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties. | eng |
dc.rights.license | Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden. | ger |
dc.subject.ddc | 510 | |
dc.subject.other | Twisted prisms | eng |
dc.subject.other | twisted prismatoids | eng |
dc.subject.other | torus knots | eng |
dc.subject.other | indecomposable polyhedra | eng |
dc.subject.other | Steiner points | eng |
dc.subject.other | Schönhardt polyhedron | eng |
dc.subject.other | Rambau polyhedron | eng |
dc.title | On decomposition of embedded prismatoids in $R^3$ without additional points | eng |
dc.type | Report | eng |
dc.type | Text | eng |
dcterms.extent | 14 S. | |
tib.accessRights | openAccess | |
wgl.contributor | WIAS | |
wgl.subject | Mathematik | |
wgl.type | Report / Forschungsbericht / Arbeitspapier |
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