# Vinberg's algorithm

In mathematics, Vinberg's algorithm is an algorithm, introduced by Ernest Borisovich Vinberg, for finding a fundamental domain of a hyperbolic reflection group.

Conway (1983) used Vinberg's algorithm to describe the automorphism group of the 26-dimensional even unimodular Lorentzian lattice II25,1 in terms of the Leech lattice.

## References

• Conway, John Horton (1983), "The automorphism group of the 26-dimensional even unimodular Lorentzian lattice", Journal of Algebra, 80 (1): 159–163, doi:10.1016/0021-8693(83)90025-X, ISSN 0021-8693, MR 0690711
• Vinberg, È. B. (1975), "Some arithmetical discrete groups in Lobačevskiĭ spaces", in Baily, Walter L. (ed.), Discrete subgroups of Lie groups and applications to moduli (Internat. Colloq., Bombay, 1973), Oxford University Press, pp. 323–348, ISBN 978-0-19-560525-9, MR 0422505