{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T03:46:19Z","timestamp":1740109579977,"version":"3.37.3"},"reference-count":32,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2020,8,31]],"date-time":"2020-08-31T00:00:00Z","timestamp":1598832000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,8,31]],"date-time":"2020-08-31T00:00:00Z","timestamp":1598832000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"crossref","award":["SFB\/TRR 109"],"award-info":[{"award-number":["SFB\/TRR 109"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"crossref"}]},{"name":"European Research Council","award":["78818 Alpha"],"award-info":[{"award-number":["78818 Alpha"]}]},{"DOI":"10.13039\/501100000923","name":"Australian Research Council","doi-asserted-by":"crossref","award":["DP1401000851"],"award-info":[{"award-number":["DP1401000851"]}],"id":[{"id":"10.13039\/501100000923","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Discrete Comput Geom"],"published-print":{"date-parts":[[2021,10]]},"DOI":"10.1007\/s00454-020-00240-w","type":"journal-article","created":{"date-parts":[[2020,8,31]],"date-time":"2020-08-31T20:03:28Z","timestamp":1598904208000},"page":"938-976","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On Mutually Diagonal Nets on (Confocal) Quadrics and 3-Dimensional Webs"],"prefix":"10.1007","volume":"66","author":[{"given":"Arseniy V.","family":"Akopyan","sequence":"first","affiliation":[]},{"given":"Alexander I.","family":"Bobenko","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7993-9632","authenticated-orcid":false,"given":"Wolfgang K.","family":"Schief","sequence":"additional","affiliation":[]},{"given":"Jan","family":"Techter","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,8,31]]},"reference":[{"issue":"4","key":"240_CR1","doi-asserted-by":"publisher","first-page":"2825","DOI":"10.1090\/tran\/7292","volume":"370","author":"AV Akopyan","year":"2018","unstructured":"Akopyan, A.V., Bobenko, A.I.: Incircular nets and confocal conics. Trans. Am. Math. Soc. 370(4), 2825\u20132854 (2018)","journal-title":"Trans. Am. Math. Soc."},{"key":"240_CR2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-2063-1","volume-title":"Mathematical Methods of Classical Mechanics. Graduate Texts in Mathematics","author":"VI Arnold","year":"1989","unstructured":"Arnold, V.I.: Mathematical Methods of Classical Mechanics. Graduate Texts in Mathematics, vol. 60. Springer, New York (1989)"},{"issue":"1","key":"240_CR3","first-page":"150","volume":"28","author":"W Blaschke","year":"1928","unstructured":"Blaschke, W.: Topologische Fragen der Differentialgeometrie. I. Thomsens Sechseckgewebe. Zueinander diagonale Netze. Math. Z. 28(1), 150\u2013157 (1928)","journal-title":"Zueinander diagonale Netze. Math. Z."},{"issue":"1","key":"240_CR4","doi-asserted-by":"publisher","first-page":"158","DOI":"10.1007\/BF01181154","volume":"28","author":"W Blaschke","year":"1928","unstructured":"Blaschke, W.: Topologische Fragen der Differentialgeometrie. II. Achtflachgewebe. Math. Z. 28(1), 158\u2013160 (1928)","journal-title":"Achtflachgewebe. Math. Z."},{"issue":"5","key":"240_CR5","first-page":"1504","volume":"2017","author":"AI Bobenko","year":"2007","unstructured":"Bobenko, A.I., Schief, W.K.: Circle complexes and the discrete CKP equation. Int. Math. Res. Not. IMRN 2017(5), 1504\u20131561 (2007)","journal-title":"Int. Math. Res. Not. IMRN"},{"key":"240_CR6","doi-asserted-by":"publisher","DOI":"10.1093\/imrn\/rny279","author":"AI Bobenko","year":"2018","unstructured":"Bobenko, A.I., Schief, W.K., Suris, Y.B., Techter, J.: On a discretization of confocal quadrics. A geometric approach to general parametrizations. Int. Math. Res. Not. IMRN (2018). https:\/\/doi.org\/10.1093\/imrn\/rny279","journal-title":"Int. Math. Res. Not. IMRN"},{"key":"240_CR7","doi-asserted-by":"publisher","first-page":"97","DOI":"10.1007\/s10711-019-00449-x","volume":"204","author":"AI Bobenko","year":"2020","unstructured":"Bobenko, A.I., Schief, W.K., Techter, J.: Checkerboard incircular nets: Laguerre geometry and parametrisation. Geom. Dedicata 204, 97\u2013129 (2020)","journal-title":"Geom. Dedicata"},{"key":"240_CR8","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-7643-8621-4","volume-title":"Discrete Differential Geometry. Integrable Structure. Graduate Studies in Mathematics","author":"AI Bobenko","year":"2008","unstructured":"Bobenko, A.I., Suris, Y.B.: Discrete Differential Geometry. Integrable Structure. Graduate Studies in Mathematics, vol. 98. American Mathematical Society, Providence (2008)"},{"key":"240_CR9","doi-asserted-by":"publisher","first-page":"326","DOI":"10.1007\/BF01220923","volume":"21","author":"W B\u00f6hm","year":"1970","unstructured":"B\u00f6hm, W.: Verwandte S\u00e4tze \u00fcber Kreisvierseitnetze. Arch. Math. (Basel) 21, 326\u2013330 (1970)","journal-title":"Arch. Math. (Basel)"},{"key":"240_CR10","volume-title":"Principes de G\u00e9om\u00e9trie Analytique","author":"G Darboux","year":"1917","unstructured":"Darboux, G.: Principes de G\u00e9om\u00e9trie Analytique. Gauthier-Villars, Paris (1917)"},{"key":"240_CR11","volume-title":"Le\u00e7ons sur la Th\u00e9orie G\u00e9n\u00e9rale des Surfaces et les Applications G\u00e9om\u00e9triques du Calcul Infinit\u00e9simal","author":"G Darboux","year":"1972","unstructured":"Darboux, G.: Le\u00e7ons sur la Th\u00e9orie G\u00e9n\u00e9rale des Surfaces et les Applications G\u00e9om\u00e9triques du Calcul Infinit\u00e9simal, vol. 2. Chelsea, Bronx (1972)"},{"key":"240_CR12","volume-title":"Ellipsoidal Harmonics. Theory and Applications. Encyclopedia of Mathematics and its Applications","author":"G Dassios","year":"2012","unstructured":"Dassios, G.: Ellipsoidal Harmonics. Theory and Applications. Encyclopedia of Mathematics and its Applications, vol. 146. Cambridge University Press, Cambridge (2012)"},{"key":"240_CR13","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-0348-0015-0","volume-title":"Poncelet Porisms and Beyond. Integrable Billiards, Hyperelliptic Jacobians and Pencils of Quadrics. Frontiers in Mathematics","author":"V Dragovi\u0107","year":"2011","unstructured":"Dragovi\u0107, V., Radnovi\u0107, M.: Poncelet Porisms and Beyond. Integrable Billiards, Hyperelliptic Jacobians and Pencils of Quadrics. Frontiers in Mathematics. Birkh\u00e4user, Basel (2011)"},{"issue":"3","key":"240_CR14","doi-asserted-by":"publisher","first-page":"213","DOI":"10.2307\/2370018","volume":"25","author":"LP Eisenhart","year":"1903","unstructured":"Eisenhart, L.P.: Isothermal-conjugate systems of lines on surfaces. Am. J. Math. 25(3), 213\u2013248 (1903)","journal-title":"Am. J. Math."},{"key":"240_CR15","volume-title":"A Treatise on the Differential Geometry of Curves and Surfaces","author":"LP Eisenhart","year":"1960","unstructured":"Eisenhart, L.P.: A Treatise on the Differential Geometry of Curves and Surfaces. Dover, New York (1960)"},{"key":"240_CR16","volume-title":"Higher Transcendental Functions","author":"A Erd\u00e9lyi","year":"1955","unstructured":"Erd\u00e9lyi, A., Magnus, W., Oberhettinger, F., Tricomi, F.G.: Higher Transcendental Functions, vol. III. McGraw-Hill, New York\u2013Toronto\u2013London (1955)"},{"key":"240_CR17","doi-asserted-by":"publisher","DOI":"10.1090\/mbk\/046","volume-title":"Mathematical Omnibus. Thirty Lectures on Classic Mathematics","author":"D Fuchs","year":"2007","unstructured":"Fuchs, D., Tabachnikov, S.: Mathematical Omnibus. Thirty Lectures on Classic Mathematics. American Mathematical Society, Providence (2007)"},{"issue":"3\u20134","key":"240_CR18","first-page":"307","volume":"53","author":"D Genin","year":"2007","unstructured":"Genin, D., Khesin, B., Tabachnikov, S.: Geodesics on an ellipsoid in Minkowski space. Enseign. Math. 53(3\u20134), 307\u2013331 (2007)","journal-title":"Enseign. Math."},{"key":"240_CR19","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-45450-3","volume-title":"The Universe of Conics","author":"G Glaeser","year":"2016","unstructured":"Glaeser, G., Stachel, H., Odehnal, B.: The Universe of Conics. Springer Spektrum, Berlin (2016)"},{"key":"240_CR20","unstructured":"Graf, H., Sauer, R.: \u00dcber dreifache Geradensysteme in der Ebene, welche Dreiecksnetze bilden. Sitzungsberichte der Bayerische Akademie der Wissenschaften zu M\u00fcnchen. Math. Naturw. Abt. 1924(2), 119\u2013156 (1924)"},{"key":"240_CR21","volume-title":"Geometry and the Imagination","author":"D Hilbert","year":"1952","unstructured":"Hilbert, D., Cohn-Vossen, S.: Geometry and the Imagination. Chelsea, New York (1952)"},{"key":"240_CR22","doi-asserted-by":"crossref","unstructured":"Izmestiev, I., Tabachnikov, S.: Ivory\u2019s theorem revisited. J. Integrable Syst. 2(1), #\u00a0xyx006 (2017)","DOI":"10.1093\/integr\/xyx006"},{"issue":"2","key":"240_CR23","doi-asserted-by":"publisher","first-page":"125","DOI":"10.1007\/BF01918987","volume":"7","author":"R Koch","year":"1976","unstructured":"Koch, R.: Diagonale Netze aus Schmieg- und Kr\u00fcmmungslinien I. J. Geom. 7(2), 125\u2013155 (1976)","journal-title":"J. Geom."},{"issue":"1\u20132","key":"240_CR24","doi-asserted-by":"publisher","first-page":"163","DOI":"10.1007\/BF01918068","volume":"9","author":"R Koch","year":"1977","unstructured":"Koch, R.: Diagonale Netze aus Schmieg- und Kr\u00fcmmungslinien. II. J. Geom. 9(1\u20132), 163\u2013194 (1977)","journal-title":"J. Geom."},{"issue":"10","key":"240_CR25","doi-asserted-by":"publisher","first-page":"895","DOI":"10.1080\/00029890.2007.11920482","volume":"114","author":"M Levi","year":"2007","unstructured":"Levi, M., Tabachnikov, S.: The Poncelet grid and billiards in ellipses. Am. Math. Monthly 114(10), 895\u2013908 (2007)","journal-title":"Am. Math. Monthly"},{"issue":"3","key":"240_CR26","doi-asserted-by":"publisher","first-page":"681","DOI":"10.1145\/1141911.1141941","volume":"25","author":"Y Liu","year":"2006","unstructured":"Liu, Y., Pottmann, H., Wallner, J., Yang, Y.-L., Wang, W.: Geometric modeling with conical meshes and developable surfaces. ACM Trans. Graphics 25(3), 681\u2013689 (2006)","journal-title":"ACM Trans. Graphics"},{"key":"240_CR27","doi-asserted-by":"crossref","unstructured":"Moser, J.: Geometry of quadrics and spectral theory. In: Proceedings of the Chern Symposium (Berkeley 1979), pp. 147\u2013188. Springer, New York\u2013Berlin (1980)","DOI":"10.1007\/978-1-4613-8109-9_7"},{"issue":"3","key":"240_CR28","doi-asserted-by":"publisher","first-page":"249","DOI":"10.1007\/s10444-007-9045-4","volume":"29","author":"H Pottmann","year":"2008","unstructured":"Pottmann, H., Wallner, J.: The focal geometry of circular and conical meshes. Adv. Comput. Math. 29(3), 249\u2013268 (2008)","journal-title":"Adv. Comput. Math."},{"issue":"1","key":"240_CR29","first-page":"41","volume":"1925","author":"R Sauer","year":"1925","unstructured":"Sauer, R.: Die Raumeinteilungen, welche durch Ebenen erzeugt werden, von denen je vier sich in einem Punkt schneiden. Sitzungsberichte der Bayerische Akademie der Wissenschaften zu M\u00fcnchen. Math. Naturw. Abt. 1925(1), 41\u201356 (1925)","journal-title":"Math. Naturw. Abt."},{"issue":"2","key":"240_CR30","doi-asserted-by":"publisher","first-page":"157","DOI":"10.1515\/ADVGEOM.2007.010","volume":"7","author":"RE Schwartz","year":"2007","unstructured":"Schwartz, R.E.: The Poncelet grid. Adv. Geom. 7(2), 157\u2013175 (2007)","journal-title":"Adv. Geom."},{"issue":"1","key":"240_CR31","doi-asserted-by":"publisher","first-page":"75","DOI":"10.2307\/2370444","volume":"39","author":"AE Young","year":"1917","unstructured":"Young, A.E.: On the determination of a certain class of surfaces. Am. J. Math. 39(1), 75\u201385 (1917)","journal-title":"Am. J. Math."},{"key":"240_CR32","unstructured":"NIST Digital Library of Mathematical Functions, National Institute of Standards and Technology, U.S. Department of Commerce (2010\u20132019). https:\/\/dlmf.nist.gov"}],"container-title":["Discrete & Computational Geometry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-020-00240-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00454-020-00240-w\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-020-00240-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,6]],"date-time":"2023-10-06T16:01:36Z","timestamp":1696608096000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00454-020-00240-w"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,8,31]]},"references-count":32,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2021,10]]}},"alternative-id":["240"],"URL":"https:\/\/doi.org\/10.1007\/s00454-020-00240-w","relation":{},"ISSN":["0179-5376","1432-0444"],"issn-type":[{"type":"print","value":"0179-5376"},{"type":"electronic","value":"1432-0444"}],"subject":[],"published":{"date-parts":[[2020,8,31]]},"assertion":[{"value":"23 August 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 March 2020","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"28 July 2020","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"31 August 2020","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}