Open AccessOn the classification of stably reflective hyperbolic Z[√2]-lattices of rank 4
Author(s) -
Nikolay Bogachev,
Nikolay Bogachev
Publication year - 2019
Publication title -
doklady akademii nauk. rossijskaâ akademiâ nauk
Language(s) - English
Resource type - Journals
ISSN - 0869-5652
DOI - 10.31857/s0869-565248617-11
Subject(s) - polyhedron , rank (graph theory) , hyperbolic space , reflection (computer programming) , mathematics , hyperbolic triangle , enhanced data rates for gsm evolution , combinatorics , hyperbolic geometry , pure mathematics , computer science , artificial intelligence , differential geometry , programming language
In this paper we prove that the fundamental polyhedron of a ℤ2-arithmetic reflection group in the three-dimensional Lobachevsky space contains an edge such that the distance between its framing faces is small enough. Using this fact we obtain a classification of stably reflective hyperbolic ℤ2-lattices of rank 4.