---
_id: '62262'
abstract:
- lang: eng
  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.
author:
- first_name: Franziska
  full_name: Stamer, Franziska
  id: '121813'
  last_name: Stamer
- first_name: 'Thomas '
  full_name: 'Titz Mite, Thomas '
  last_name: Titz Mite
citation:
  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} }'
  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.
  mla: Stamer, Franziska, and Thomas Titz Mite. <i>On Chamber-Regular C̃₂-Lattices</i>.
    2025.
  short: F. Stamer, T. Titz Mite, (2025).
date_created: 2025-11-19T15:09:51Z
date_updated: 2025-11-26T15:09:58Z
department:
- _id: '10'
external_id:
  arxiv:
  - '2511.08312'
language:
- iso: eng
page: '29'
status: public
title: On Chamber-regular C̃₂-Lattices
type: preprint
user_id: '121813'
year: '2025'
...