The paper provides the Coxeter schemes of all the discrete groups generated by reflections in the faces of simplicial prisms the combinatory type of which is the product of a simplex and a segment in Lobachevskian spaces.
This is a preview of subscription content, access via your institution.
Buy single article
Instant access to the full article PDF.
Price excludes VAT (USA)
Tax calculation will be finalised during checkout.
B. A. Rozenfel'd, Noneuclidean Spaces [in Russian], Moscow (1969).
H. S. M. Coxeter, “Discrete groups generated by reflections,” Ann. Math.,35, No. 3, 588–624 (1934).
F. Lanner, “On complexes with transitive groups of automorphisms,” Lund (1950).
V. S. Makarov, “On one class of partitions of Lobachevskian space,” Dokl. Akad. Nauk SSSR,161, No. 2, 277, 278 (1965).
V. S. Makarov, “On one class of discrete groups of Lobachevskian space having an infinite fundamental region of finite measure,” Dokl. Akad. Nauk SSSR,167, No. 1, 30–33 (1966).
V. S. Makarov, “On Fedorov groups of four-dimensional and five-dimensional Lobachevskian spaces,” in: Investigations in Higher Algebra [in Russian], Kishinev (1968), Vol. 1.
É. B. Vinberg, “Discrete groups generated by reflections in Lobachevskian spaces,” Matem. Sb.,72 (114), No. 3, 471–488 (1967).
É. B. Vinberg, “Some examples of crystallographic groups in Lobachevskian spaces,” Matem. Sb.,78 (120), No. 4, 633–639 (1969).
E. M. Andreev, “On convex polyhedra in Lobachevskian spaces,” Matem. Sb.,81 (123), No. 3, 445–478 (1970).
E. M. Andreev, “The intersection of faces of polyhedra with acute angles,” Matem. Zametki,8, No. 4, 521–527 (1970).
Translated from Matematicheskie Zametki, Vol. 15, No. 1, pp. 159–164, January, 1974.
In conclusion, the author wishes to express gratitude for the direction of É. B. Vinberg.
About this article
Cite this article
Kaplinskaya, I.M. Discrete groups generated by reflections in the faces of symplicial prisms in Lobachevskian spaces. Mathematical Notes of the Academy of Sciences of the USSR 15, 88–91 (1974). https://doi.org/10.1007/BF01153552