[{"status":"public","abstract":[{"text":"We construct the first examples of chamber-regular lattices on C̃₂-buildings. Assuming a conjecture of Kantor our list of examples becomes a classification for chamber-regular C̃₂-lattices on locally-finite C̃₂-buildings. The links of special vertices in the buildings we construct, are all isomorphic to (the incidence graph of) the unique generalized quadrangle Q of order (3,5). In particular our constructions involve chamber-regular actions on Q. These actions on Q are the first (and if Kantor's conjecture holds the only) chamber-regular actions on a finite generalized quadrangle and therefore interesting in their own right. Moreover Q is not Moufang and therefore none of our examples is a Bruhat-Tits building and all our lattices are exotic building lattices.","lang":"eng"}],"type":"preprint","language":[{"iso":"eng"}],"user_id":"121813","department":[{"_id":"10"}],"_id":"62262","external_id":{"arxiv":["2511.08312"]},"citation":{"chicago":"Stamer, Franziska, and Thomas  Titz Mite. “On Chamber-Regular C̃₂-Lattices,” 2025.","ieee":"F. Stamer and T. Titz Mite, “On Chamber-regular C̃₂-Lattices.” 2025.","ama":"Stamer F, Titz Mite T. On Chamber-regular C̃₂-Lattices. Published online 2025.","apa":"Stamer, F., &#38; Titz Mite, T. (2025). <i>On Chamber-regular C̃₂-Lattices</i>.","bibtex":"@article{Stamer_Titz Mite_2025, title={On Chamber-regular C̃₂-Lattices}, author={Stamer, Franziska and Titz Mite, Thomas }, year={2025} }","short":"F. Stamer, T. Titz Mite, (2025).","mla":"Stamer, Franziska, and Thomas Titz Mite. <i>On Chamber-Regular C̃₂-Lattices</i>. 2025."},"page":"29","year":"2025","title":"On Chamber-regular C̃₂-Lattices","date_created":"2025-11-19T15:09:51Z","author":[{"id":"121813","full_name":"Stamer, Franziska","last_name":"Stamer","first_name":"Franziska"},{"full_name":"Titz Mite, Thomas ","last_name":"Titz Mite","first_name":"Thomas "}],"date_updated":"2025-11-26T15:09:58Z"}]