Geodesic
Coxeter Decompositions of Compact Hyperbolic Pyramids and Triangular Prisms
Matematičeskie zametki, Tome 75 (2004) no. 4, pp. 624-636 
A. A. Felikson. Coxeter Decompositions of Compact Hyperbolic Pyramids and Triangular Prisms. Matematičeskie zametki, Tome 75 (2004) no. 4, pp. 624-636. http://geodesic.mathdoc.fr/item/MZM_2004_75_4_a11/
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     author = {A. A. Felikson},
     title = {Coxeter {Decompositions} of {Compact} {Hyperbolic} {Pyramids} and {Triangular} {Prisms}},
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Voir la notice de l'article provenant de la source Math-Net.Ru

A polyhedron P admits a Coxeter decomposition if P can be tiled by finitely many Coxeter polyhedra such that any two tiles having a common face are symmetric with respect to this face. In this paper, we classify Coxeter decompositions of compact convex pyramids and triangular prisms in the hyperbolic space $\mathbb H^3$.

[1] Schwarz H. A, “Über diejenige Fälle in welchen die Gaussische hypergeometrische Reihe eine algeraische Function ihres viertes elementes darstellt”, Crelle's J., 75 (1873), 292–335

[2] Klimenko E., Sakuma M., “Two-generator discrete subgroups of $\operatorname{Isom}(\mathbb H^2)$ containing orientation-reversing elements”, Geom. Dedicata, 72 (1998), 247–282 | DOI | MR | Zbl

[3] Felikson A., Coxeter decompositions of hyperbolic tetrahedra, , 2002 E-print math.MG/0212010

[4] Felikson A., “Koksterovskie razbieniya giperbolicheskikh simpleksov”, Matem. sb., 193:12 (2002), 134–156 | MR | Zbl

[5] Andreev E. M., “O peresechenii ploskostei granei mnogogrannikov s ostrymi uglami”, Matem. zametki, 8:4 (1970), 521–527 | MR | Zbl

[6] Felikson A., Coxeter decompositions of hyperbolic pyramids and triangular prisms, , 2002 E-print math.MG/0212195

[7] Andreev E. M., “O vypuklykh mnogogrannikakh v prostranstvakh Lobachevskogo”, Matem. sb., 81:3 (1970), 445–478 | MR | Zbl