{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,20]],"date-time":"2026-02-20T18:30:08Z","timestamp":1771612208450,"version":"3.50.1"},"reference-count":41,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2018,12,17]],"date-time":"2018-12-17T00:00:00Z","timestamp":1545004800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Period Math Hung"],"published-print":{"date-parts":[[2019,9]]},"DOI":"10.1007\/s10998-018-00277-8","type":"journal-article","created":{"date-parts":[[2018,12,17]],"date-time":"2018-12-17T05:55:40Z","timestamp":1545026140000},"page":"32-49","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["On volumes of truncated tetrahedra with constrained edge lengths"],"prefix":"10.1007","volume":"79","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2692-6584","authenticated-orcid":false,"given":"R.","family":"Frigerio","sequence":"first","affiliation":[]},{"given":"Marco","family":"Moraschini","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2018,12,17]]},"reference":[{"issue":"5","key":"277_CR1","doi-asserted-by":"publisher","first-page":"1139","DOI":"10.2307\/2375068","volume":"115","author":"A Basmajian","year":"1993","unstructured":"A. Basmajian, The orthogonal spectrum of a hyperbolic manifold. Am. J. Math. 115(5), 1139\u20131159 (1993)","journal-title":"Am. J. Math."},{"key":"277_CR2","doi-asserted-by":"publisher","first-page":"1210","DOI":"10.1007\/s00039-010-0095-2","volume":"20","author":"M Bridgeman","year":"2010","unstructured":"M. Bridgeman, J. Kahn, Hyperbolic volume of manifolds with geodesic boundary and orthospectra. Geom. Funct. Anal. 20, 1210\u20131230 (2010)","journal-title":"Geom. Funct. Anal."},{"key":"277_CR3","doi-asserted-by":"publisher","first-page":"317","DOI":"10.1137\/060669073","volume":"51","author":"J Brandts","year":"2009","unstructured":"J. Brandts, S. Korotov, M. Kr\u00edzek, J. Solc, On nonobtuse simplicial partitions. SIAM Rev. 51, 317\u2013335 (2009)","journal-title":"SIAM Rev."},{"key":"277_CR4","doi-asserted-by":"publisher","first-page":"707","DOI":"10.2140\/gt.2011.15.707","volume":"15","author":"M Bridgeman","year":"2011","unstructured":"M. Bridgeman, Orthospectra of geodesic laminations and dilogarithm identities on moduli space. Geom. Topol. 15, 707\u2013733 (2011)","journal-title":"Geom. Topol."},{"issue":"1","key":"277_CR5","doi-asserted-by":"publisher","first-page":"491","DOI":"10.2140\/gt.2014.18.491","volume":"18","author":"M Bridgeman","year":"2014","unstructured":"M. Bridgeman, S.P. Tan, Moments of the boundary hitting function for the geodesic flow on a hyperbolic manifold. Geom. Topol. 18(1), 491\u2013520 (2014)","journal-title":"Geom. Topol."},{"key":"277_CR6","doi-asserted-by":"crossref","unstructured":"M. Bridgeman, S.P. Tan, Handbook of Teichm\u00fcller Theory. IRMA lectures in mathematics and theoretical physics, identities on hyperbolic manifolds, vol.\u00a026 (European Mathematical Society, Z\u00fcrich, 2016) (pp. 19\u201353)","DOI":"10.4171\/160-1\/2"},{"issue":"2010","key":"277_CR7","doi-asserted-by":"publisher","first-page":"1857","DOI":"10.2140\/agt.2010.10.1857","volume":"10","author":"D Calegari","year":"2010","unstructured":"D. Calegari, Chimneys, leopard spots and the identities of Basmajian and Bridgeman. Algebraic Geom. Topol. 10(2010), 1857\u20131863 (2010)","journal-title":"Algebraic Geom. Topol."},{"key":"277_CR8","first-page":"173","volume":"38","author":"D Calegari","year":"2011","unstructured":"D. Calegari, Bridgeman\u2019s orthospectrum identity. Topol. Proc. 38, 173\u2013179 (2011)","journal-title":"Topol. Proc."},{"key":"277_CR9","doi-asserted-by":"publisher","first-page":"385","DOI":"10.1007\/s10711-015-0086-4","volume":"179","author":"F Costantino","year":"2015","unstructured":"F. Costantino, F. Gu\u00e9ritaud, R. van der Veen, On the volume conjecture for polyhedra. Geom. Dedic. 179, 385\u2013409 (2015)","journal-title":"Geom. Dedic."},{"key":"277_CR10","unstructured":"Q. Chen, J. Murakami, Asymptotics of quantum \n                    \n                      \n                    \n                    $$6j-$$\n                    \n                      \n                        \n                          6\n                          j\n                          -\n                        \n                      \n                    \n                  symbols. \n                    arXiv:1706.04887"},{"key":"277_CR11","doi-asserted-by":"publisher","first-page":"303","DOI":"10.4171\/QT\/41","volume":"4","author":"F Costantino","year":"2013","unstructured":"F. Costantino, J. Murakami, On the \n                    \n                      \n                    \n                    $$sl(2,\\mathbb{C})$$\n                    \n                      \n                        \n                          s\n                          l\n                          (\n                          2\n                          ,\n                          C\n                          )\n                        \n                      \n                    \n                   quantum \n                    \n                      \n                    \n                    $$6j-$$\n                    \n                      \n                        \n                          6\n                          j\n                          -\n                        \n                      \n                    \n                  symbols and their relation to the hyperbolic volume. Quantum Topol. 4, 303\u2013351 (2013)","journal-title":"Quantum Topol."},{"key":"277_CR12","doi-asserted-by":"publisher","first-page":"1831","DOI":"10.2140\/gt.2007.11.1831","volume":"11","author":"F Costantino","year":"2007","unstructured":"F. Costantino, \n                    \n                      \n                    \n                    $$6j-$$\n                    \n                      \n                        \n                          6\n                          j\n                          -\n                        \n                      \n                    \n                  symbols, hyperbolic structures and the volume conjecture. Geom. Topol. 11, 1831\u20131854 (2007)","journal-title":"Geom. Topol."},{"key":"277_CR13","unstructured":"R. Frigerio, M. Moraschini, The ideal simplicial volume of manifolds with boundary. Int. Math. Res. Not. IMRN (to appear)"},{"key":"277_CR14","doi-asserted-by":"publisher","first-page":"171","DOI":"10.1080\/10586458.2004.10504531","volume":"13","author":"R Frigerio","year":"2004","unstructured":"R. Frigerio, B. Martelli, C. Petronio, Small hyperbolic 3-manifolds with geodesic boundary. Exp. Math. 13, 171\u2013184 (2004)","journal-title":"Exp. Math."},{"key":"277_CR15","doi-asserted-by":"publisher","first-page":"3243","DOI":"10.1090\/S0002-9947-03-03378-6","volume":"356","author":"R Frigerio","year":"2003","unstructured":"R. Frigerio, C. Petronio, Construction and recognition of hyperbolic \n                    \n                      \n                    \n                    $$3$$\n                    \n                      \n                        \n                          3\n                        \n                      \n                    \n                  -manifolds with geodesic boundary. Trans. Am. Math. Soc. 356, 3243\u20133282 (2003)","journal-title":"Trans. Am. Math. Soc."},{"key":"277_CR16","doi-asserted-by":"publisher","first-page":"139","DOI":"10.1007\/s10711-010-9561-0","volume":"153","author":"R Guo","year":"2011","unstructured":"R. Guo, Calculus of generalized hyperbolic tetrahedra. Geom. Dedic. 153, 139\u2013149 (2011)","journal-title":"Geom. Dedic."},{"key":"277_CR17","first-page":"109","volume":"11","author":"H Hadwiger","year":"1956","unstructured":"H. Hadwiger, Ungel\u00f6ste probleme. Elem. Math. 11, 109\u2013110 (1956)","journal-title":"Elem. Math."},{"key":"277_CR18","doi-asserted-by":"publisher","first-page":"97","DOI":"10.1007\/s00010-011-0100-3","volume":"83","author":"\u00c1G Horv\u00e1th","year":"2012","unstructured":"\u00c1.G. Horv\u00e1th, Formulas on hyperbolic volumes. Aequat. Math. 83, 97\u2013116 (2012)","journal-title":"Aequat. Math."},{"key":"277_CR19","doi-asserted-by":"publisher","first-page":"541","DOI":"10.1007\/BF01452047","volume":"245","author":"R Kellerhals","year":"1989","unstructured":"R. Kellerhals, On the volume of hyperbolic polyhedra. Math. Ann. 245, 541\u2013569 (1989)","journal-title":"Math. Ann."},{"key":"277_CR20","first-page":"301","volume-title":"The Dilogarithm and Volumes of Hyperbolic Polytopes, Mathematical Surveys and Monographs","author":"R Kellerhals","year":"1991","unstructured":"R. Kellerhals, The Dilogarithm and Volumes of Hyperbolic Polytopes, Mathematical Surveys and Monographs, vol. 37 (Americal Mathematical Society, New York, 1991), pp. 301\u2013336"},{"key":"277_CR21","doi-asserted-by":"publisher","first-page":"640","DOI":"10.1007\/BF01902056","volume":"5","author":"R Kellerhals","year":"1995","unstructured":"R. Kellerhals, Volumes in hyperbolic 5-space. Geom. Funct. Anal. 5, 640\u2013667 (1995)","journal-title":"Geom. Funct. Anal."},{"key":"277_CR22","doi-asserted-by":"publisher","first-page":"175","DOI":"10.4310\/jdg\/1214446997","volume":"34","author":"S Kojima","year":"1991","unstructured":"S. Kojima, Y. Miyamoto, The smallest hyperbolic 3-manifolds with totally geodesic boundary. J. Differ. Geom. 34, 175\u2013192 (1991)","journal-title":"J. Differ. Geom."},{"key":"277_CR23","doi-asserted-by":"publisher","first-page":"449","DOI":"10.1007\/s00010-012-0153-y","volume":"85","author":"A Kolpakov","year":"2013","unstructured":"A. Kolpakov, J. Murakami, Volume of a doubly truncated hyperbolic tetrahedron. Aequat. Math. 85, 449\u2013463 (2013)","journal-title":"Aequat. Math."},{"key":"277_CR24","first-page":"37","volume":"10","author":"S Kojima","year":"1990","unstructured":"S. Kojima, Polyhedral decomposition of hyperbolic manifolds with boundary. Proc. Work. Pure Math. 10, 37\u201357 (1990)","journal-title":"Proc. Work. Pure Math."},{"key":"277_CR25","doi-asserted-by":"publisher","first-page":"93","DOI":"10.2969\/aspm\/02010093","volume":"20","author":"S Kojima","year":"1992","unstructured":"S. Kojima, Polyhedral decomposition of hyperbolic 3-manifolds with totally geodesic boundary, aspects of low-dimensional manifolds. Adv. Stud. Pure Math. 20, 93\u2013112 (1992)","journal-title":"Adv. Stud. Pure Math."},{"key":"277_CR26","doi-asserted-by":"publisher","first-page":"12","DOI":"10.1090\/S1079-6762-05-00142-3","volume":"11","author":"F Luo","year":"2005","unstructured":"F. Luo, A combinatorial curvature flow for compact 3-manifolds with boundary. Electron. Res. Announc. Am. Math. Soc. 11, 12\u201320 (2005)","journal-title":"Electron. Res. Announc. Am. Math. Soc."},{"key":"277_CR27","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1112\/topo.12046","volume":"11","author":"F Luo","year":"2018","unstructured":"F. Luo, T. Yang, Volume and rigidity of hyperbolic polyhedral 3-manifolds. J. Topol. 11, 1\u201329 (2018)","journal-title":"J. Topol."},{"key":"277_CR28","first-page":"281","volume-title":"The Schl\u00e4fli Differential Formula, Collected Papers","author":"JW Milnor","year":"1994","unstructured":"J.W. Milnor, The Schl\u00e4fli Differential Formula, Collected Papers, vol. 1 (Geometry, Publish or Perish Inc, Houston, 1994), pp. 281\u2013295"},{"key":"277_CR29","doi-asserted-by":"publisher","first-page":"223","DOI":"10.1007\/BF00145916","volume":"40","author":"Y Miyamoto","year":"1991","unstructured":"Y. Miyamoto, On the volume and surface area of hyperbolic polyhedra. Geom. Dedic. 40, 223\u2013236 (1991)","journal-title":"Geom. Dedic."},{"key":"277_CR30","doi-asserted-by":"publisher","first-page":"613","DOI":"10.1016\/0040-9383(94)90001-9","volume":"33","author":"Y Miyamoto","year":"1994","unstructured":"Y. Miyamoto, Volumes of hyperbolic manifolds with geodesic boundary. Topology 33, 613\u2013629 (1994)","journal-title":"Topology"},{"key":"277_CR31","first-page":"127","volume":"32","author":"E Moln\u00e1r","year":"1989","unstructured":"E. Moln\u00e1r, Projective metrics and hyperbolic volume. Ann. Univ. Sci. Budapest. E\u00f6tv\u00f6s Sect. Math. 32, 127\u2013157 (1989)","journal-title":"Ann. Univ. Sci. Budapest. E\u00f6tv\u00f6s Sect. Math."},{"key":"277_CR32","doi-asserted-by":"publisher","first-page":"153","DOI":"10.1007\/s00022-005-0010-4","volume":"83","author":"J Murakami","year":"2005","unstructured":"J. Murakami, A. Ushijima, A volume formula for hyperbolic tetrahedra in terms of edge lengths. J. Geom. 83, 153\u2013163 (2005)","journal-title":"J. Geom."},{"key":"277_CR33","doi-asserted-by":"publisher","first-page":"193","DOI":"10.1007\/s10711-012-9745-x","volume":"163","author":"A Przeworski","year":"2013","unstructured":"A. Przeworski, An upper bound on density for packings of collars about hyperplanes in \n                    \n                      \n                    \n                    $$\\mathbb{H}^n$$\n                    \n                      \n                        \n                          \n                            H\n                          \n                          n\n                        \n                      \n                    \n                  . Geom. Dedic. 163, 193\u2013213 (2013)","journal-title":"Geom. Dedic."},{"key":"277_CR34","doi-asserted-by":"publisher","first-page":"73","DOI":"10.1007\/s10711-007-9217-x","volume":"131","author":"I Rivin","year":"2008","unstructured":"I. Rivin, Volumes of degenerating polyhedra\u2014on a conjecture of J.\u00a0W.\u00a0Milnor. Geom. Dedic. 131, 73\u201385 (2008)","journal-title":"Geom. Dedic."},{"key":"277_CR35","unstructured":"J.M. Schlenker, Hyperideal polyhedra in hyperbolic manifolds. \n                    arXiv:math\/0212355"},{"key":"277_CR36","doi-asserted-by":"publisher","first-page":"85","DOI":"10.4310\/MRL.2005.v12.n1.a9","volume":"12","author":"J-M Schlenker","year":"2005","unstructured":"J.-M. Schlenker, Hyperideal circle patterns. Math. Res. Lett. 12, 85\u2013102 (2005)","journal-title":"Math. Res. Lett."},{"key":"277_CR37","doi-asserted-by":"publisher","first-page":"47","DOI":"10.1007\/s00454-007-9045-7","volume":"40","author":"J-M Schlenker","year":"2008","unstructured":"J.-M. Schlenker, Circle patterns on singular surfaces. Discrete Comput. Geom. 40, 47\u2013102 (2008)","journal-title":"Discrete Comput. Geom."},{"key":"277_CR38","doi-asserted-by":"publisher","first-page":"333","DOI":"10.4310\/jdg\/1203000270","volume":"78","author":"BA Springborn","year":"2008","unstructured":"B.A. Springborn, A variational principle for weighted Delaunay triangulations and hyperideal polyhedra. J. Differ. Geom. 78, 333\u2013367 (2008)","journal-title":"J. Differ. Geom."},{"issue":"3","key":"277_CR39","first-page":"211","volume":"70","author":"J Szirmai","year":"2018","unstructured":"J. Szirmai, Hyperball packings in hyperbolic 3-space. Mat. Vesn. 70(3), 211\u2013222 (2018)","journal-title":"Mat. Vesn."},{"key":"277_CR40","first-page":"1","volume":"35","author":"K Tschirpke","year":"1994","unstructured":"K. Tschirpke, The dissection of five-dimensional simplices into orthoschemes. Beitr. Algebra Geom. 35, 1\u201311 (1994)","journal-title":"Beitr. Algebra Geom."},{"key":"277_CR41","doi-asserted-by":"crossref","unstructured":"A. Ushijima, A Volume Formula for Generalised Hyperbolic Tetrahedra, Non-Euclidean Geometries. Mathematics Application, vol. 581 (Springer, New York, 2006), pp. 249\u2013265","DOI":"10.1007\/0-387-29555-0_13"}],"container-title":["Periodica Mathematica Hungarica"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10998-018-00277-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10998-018-00277-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10998-018-00277-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,12,16]],"date-time":"2019-12-16T19:21:40Z","timestamp":1576524100000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10998-018-00277-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,12,17]]},"references-count":41,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2019,9]]}},"alternative-id":["277"],"URL":"https:\/\/doi.org\/10.1007\/s10998-018-00277-8","relation":{},"ISSN":["0031-5303","1588-2829"],"issn-type":[{"value":"0031-5303","type":"print"},{"value":"1588-2829","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,12,17]]},"assertion":[{"value":"17 December 2018","order":1,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}