Geodesic
On Some Series of Regular Tilings of the Lobachevskii Space
Informatics and Automation, Discrete geometry and geometry of numbers, Tome 239 (2002), pp. 239-250.

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Countable series of tilings of the Lobachevskii space $\Lambda ^n$ by infinite polyhedra of finite volume are constructed for $n=3,4,5,6$. 
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P. V. Makarov. On Some Series of Regular Tilings of the Lobachevskii Space. Informatics and Automation, Discrete geometry and geometry of numbers, Tome 239 (2002), pp. 239-250. http://geodesic.mathdoc.fr/item/TRSPY_2002_239_a14/

[1] Makarov P. V., “On infinite series of regular noncompact partitions of Lobachevsky–Bolyai hyperbolic space $H^n$, $n=3,4,5,6$, into infinite polytopes of finite measure”, Intern. Conf. on packings, coverings and tilings, Abstr., Budapest, Hung., 1996, 22

[2] Makarov P. V., “O postroenii schetnoi serii normalnykh pravilnykh razbienii shestimernogo prostranstva Lobachevskogo”, Sbornik trudov seminara po diskretnoi matematike i ee prilozheniyam (Moskva, 2–6 fevr. 1998 g.), Izd-vo Tsentra prikl. issled. mekh.-mat. fak. MGU, M. (to appear)

[3] Makarov P. V., “Ob odnoi schetnoi serii kristallograficheskikh razbienii pyatimernogo prostranstva Lobachevskogo”, Diskretnaya matematika i ee prilozheniya, Mater. VII Mezhdunar. seminara (Moskva, 29 yanv.–2 fevr. 2001 g.), Izd-vo Tsentra prikl. issled. mekh.-mat. fak. MGU, M., 2002, 274–278

[4] Makarov V. S., “O fedorovskikh gruppakh chetyrekhmernogo i pyatimernogo prostranstva Lobachevskogo”, Issledovaniya po obschei algebre, no. 1, Kishinev. gos. un-t, Kishinev, 1968, 120–129 | MR

[5] Makarov V. S., “O rasshirenii diskretnykh grupp ploskosti Lobachevskogo do prostranstvennykh”, Uchen. zap. Kishinev. gos. un-ta, 82, 1965, 56–59 | MR

[6] Makarov V. S., “Ob odnom klasse diskretnykh grupp prostranstva Lobachevskogo, imeyuschikh beskonechnuyu fundamentalnuyu oblast konechnoi mery”, DAN SSSR, 167:1 (1966), 30–33 | MR | Zbl

[7] Makarov V. S., “Ob odnom klasse dvumernykh fedorovskikh grupp”, Izv. AN SSSR. Ser. mat., 31:3 (1967), 531–542 | MR | Zbl

[8] Makarov V. S., “Geometricheskie metody postroeniya diskretnykh grupp dvizhenii prostranstva Lobachevskogo”, Itogi nauki i tekhniki. Problemy geometrii, 15, VINITI, M., 1983, 3–59

[9] Coxeter H. S. M., Regular polytopes, Macmillan, New York, London, 1963, 321 pp. | MR | Zbl

[10] Schlegel V., “Theorie der homogenzusammengesetzen Raumgebilde”, Nova Acta Leop. Carol., 44 (1883), 343–459

[11] Sullivan D., “Travaux de Thurston sur les groupes quasi-Fuchsiens et les varietes hyperboliques de dimension 3 fibrees sur $S^1$”, Sém. Bourbaki 1979/80. 32e ann. Exp. 554, Lect. Notes Math., 842, 1981, 196–214 | MR | Zbl

[12] Damian F. L., “K postroeniyu giperbolicheskikh chetyrekhmernykh mnogoobrazii”, Geometriya diskretnykh grupp, Mat. issledovaniya, 119, Shtiintsa, Kishinev, 1990, 79–85 | MR

[13] Kokseter G. S. M., Vvedenie v geometriyu, Nauka, M., 1966, 648 pp. | MR

[14] Gosset T., “On the regular and semi-regular figures in space of $n$ dimensions”, Mess. Math., 29 (1900), 43–48

[15] Makarov P. V., Arkhimedovy razbieniya trekhmernykh prostranstv postoyannoi krivizny, Dis. $\dots$ kand. fiz.-mat. nauk, MIAN SSSR, M., 1990, 123 pp.