Geodesic
Coxeter Decompositions of Compact Hyperbolic Pyramids and Triangular Prisms
Matematičeskie zametki, Tome 75 (2004) no. 4, pp. 624-636

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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 $\mathbb H^3$. 
@article{MZM_2004_75_4_a11,
     author = {A. A. Felikson},
     title = {Coxeter {Decompositions} of {Compact} {Hyperbolic} {Pyramids} and {Triangular} {Prisms}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {624--636},
     publisher = {mathdoc},
     volume = {75},
     number = {4},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2004_75_4_a11/}
}
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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/