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Two-sided bounds for the volume of right-angled hyperbolic polyhedraVesnin, Andreî Jurʹevič, 1963- ; Repovš, Dušan, 1954-Za poljuben kompakten pravokoten polieder ▫$R$▫ v prostoru Lobačevskega ▫${\mathbb H}^3$▫ naj ▫${\rm{vol}}(R)$▫ označuje njegovo prostornino in ▫${\rm{vert}}(R)$▫ število njegovih oglišč. Atkinson je ... nedavno našel zgornjo in spodnjo mejo za vrednosti ▫${\rm{vol}}(R)$▫, izraženi s pomočjo ▫${\rm{vert}}(R)$▫. S konstrukcijo dvoparametrične družine poliedrov v članku dokažemo, da je asimptotična zgornja meja ▫$5v_3/8$▫, kjer ▫$v_3$▫ označuje prostornino idealnega pravilnega tetraedra v ▫${\mathbb H}^3$▫, dvojna limitna točka kvocientov ▫${\rm{vol}}(R)/{\rm{vert}}(R)$▫. Poleg tega v članku izboljšamo spodnjo mejo za primer, ko je ▫${\rm{vert}}(R) \leqslant 56$▫.Source: Mathematical notes = Matematicheskie zametki. - ISSN 1067-9073 (Vol. 89, no. 1, 2011, str. 31-36)Type of material - article, component partPublish date - 2011Language - englishCOBISS.SI-ID - 15843929
Author
Vesnin, Andreî Jurʹevič, 1963- |
Repovš, Dušan, 1954-
Topics
matematika |
topologija |
hiperbolična 3-mnogoterost |
3-dimenzionalni prostor Lobačevskega |
asimptotična ocena za prostornino |
hiperbolični polieder |
pravilni polieder |
dvanajsterec |
mathematics |
topology |
hyperbolic 3-manifold |
3-dimensional Lobachevski space |
asymptotic volume estimate |
right-angled hyperbolic polyhedron |
regular polyhedron |
volume estimate for hyperbolic polyhedra |
Lobachevskii space |
Löbell polyhedron |
dodecahedron
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Vesnin, Andreî Jurʹevič, 1963- | |
Repovš, Dušan, 1954- | 07083 |
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