# 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 II_{25,1} 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

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