Geodesic
Hyperbolic octahedron with $mmm$-symmetry
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 10 (2013), pp. 123-140

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We consider hyperbolic octahedra with $mmm$-symmetry. We provide an existence theorem for them and establish trigonometrical identities involving lengths of edges and dihedral angles (the sine-tangent rules). Then we apply the Schläfli formula to find the volume of prescribed octahedra in terms of dihedral angles explicitly.
Keywords: hyperbolic octahedron, mmm-symmetry, hyperbolic volume, existence theorem
Mots-clés : sine-tangent rule. 
@article{SEMR_2013_10_a26,
     author = {N. V. Abrosimov and G. A. Baigonakova},
     title = {Hyperbolic octahedron with $mmm$-symmetry},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {123--140},
     publisher = {mathdoc},
     volume = {10},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2013_10_a26/}
}
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N. V. Abrosimov; G. A. Baigonakova. Hyperbolic octahedron with $mmm$-symmetry. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 10 (2013), pp. 123-140. http://geodesic.mathdoc.fr/item/SEMR_2013_10_a26/