Original scientific paper

On Regular Square Prism Tilings in \widetilde{SL_2R} Space

János Pallagi ; Budapest University of Technology and Economics, Institute of Mathematics, Department of Geometry, Budapest, Hungary
Benedek Schultz ; Budapest University of Technology and Economics, Institute of Mathematics, Department of Geometry, Budapest, Hungary
Jenö Szirmai orcid.org/0000-0001-9610-7993 ; Budapest University of Technology and Economics, Institute of Mathematics, Department of Geometry, Budapest, Hungary

Abstract

In [9] and [10] we have studied the regular prisms and prism tilings and their geodesic ball packings in \widetilde{SL_2R} space that is one among the eight Thurston geometries. This geometry can be derived from the 3-dimensional Lie group of all 2 ×2 real matrices with determinant one. In this paper we consider the regular infinite and bounded square prism tilings whose existence was proved in [9]. We determine the data of the above tilings and visualize them in the hyperboloid model of \widetilde{SL_2R} space.
We use for the computations and visualization of the \widetilde{SL_2R} space its projective model introduced by E. Molnár.

Keywords

Thurston geometries; \widetilde{SL_2R} geometry; tiling; prism tiling

Hrčak ID:

96185

URI

https://hrcak.srce.hr/96185

Publication date:

30.1.2013.

Article data in other languages: croatian

Visits: 1.289 *