Geodesic
The volume of a hyperbolic antipodal octahedron
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 19 (2022) no. 2, pp. 949-958

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We consider the hyperbolic antipodal octahedron. It is an octahedron with antipodal symmetry in the hyperbolic space $\mathbb{H}^3$. We establish necessary and sufficient conditions for the existence of such an octahedron in $\mathbb{H}^3$. By dividing the octahedron into appropriate tetrahedra we obtain an explicit integral formula for the volume of the hyperbolic antipodal octahedron.
Keywords: hyperbolic octahedron, hyperbolic volume, antipodal symmetry, hyperbolic tetrahedron, integral formula. 
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     author = {B. Vuong},
     title = {The volume of a hyperbolic antipodal octahedron},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
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     publisher = {mathdoc},
     volume = {19},
     number = {2},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2022_19_2_a24/}
}
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B. Vuong. The volume of a hyperbolic antipodal octahedron. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 19 (2022) no. 2, pp. 949-958. http://geodesic.mathdoc.fr/item/SEMR_2022_19_2_a24/