--- res: bibo_abstract: - Canonical parametrisations of classical confocal coordinate systems are introduced and exploited to construct non-planar analogues of incircular (IC) nets on individual quadrics and systems of confocal quadrics. Intimate connections with classical deformations of quadrics that are isometric along asymptotic lines and circular cross-sections of quadrics are revealed. The existence of octahedral webs of surfaces of Blaschke type generated by asymptotic and characteristic lines that are diagonally related to lines of curvature is proved theoretically and established constructively. Appropriate samplings (grids) of these webs lead to three-dimensional extensions of non-planar IC nets. Three-dimensional octahedral grids composed of planes and spatially extending (checkerboard) IC-nets are shown to arise in connection with systems of confocal quadrics in Minkowski space. In this context, the Laguerre geometric notion of conical octahedral grids of planes is introduced. The latter generalise the octahedral grids derived from systems of confocal quadrics in Minkowski space. An explicit construction of conical octahedral grids is presented. The results are accompanied by various illustrations which are based on the explicit formulae provided by the theory.@eng bibo_authorlist: - foaf_Person: foaf_givenName: Arseniy foaf_name: Akopyan, Arseniy foaf_surname: Akopyan foaf_workInfoHomepage: http://www.librecat.org/personId=430D2C90-F248-11E8-B48F-1D18A9856A87 orcid: 0000-0002-2548-617X - foaf_Person: foaf_givenName: Alexander I. foaf_name: Bobenko, Alexander I. foaf_surname: Bobenko - foaf_Person: foaf_givenName: Wolfgang K. foaf_name: Schief, Wolfgang K. foaf_surname: Schief - foaf_Person: foaf_givenName: Jan foaf_name: Techter, Jan foaf_surname: Techter bibo_doi: 10.1007/s00454-020-00240-w bibo_volume: 66 dct_date: 2021^xs_gYear dct_identifier: - UT:000564488500002 dct_isPartOf: - http://id.crossref.org/issn/0179-5376 - http://id.crossref.org/issn/1432-0444 dct_language: eng dct_publisher: Springer Nature@ dct_title: On mutually diagonal nets on (confocal) quadrics and 3-dimensional webs@ ...