Geodesic
On the volume formula for hyperbolic $4$-dimensional simplex
Contemporary Mathematics. Fundamental Directions, Differential and functional differential equations, Tome 63 (2017) no. 3, pp. 494-503

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In this paper, we derive an explicit formula for the volume of abritrary hyperbolic $4$-simplex depending on vertices coordinates. 
@article{CMFD_2017_63_3_a6,
     author = {V. A. Krasnov},
     title = {On the volume formula for hyperbolic $4$-dimensional simplex},
     journal = {Contemporary Mathematics. Fundamental Directions},
     pages = {494--503},
     publisher = {mathdoc},
     volume = {63},
     number = {3},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2017_63_3_a6/}
}
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V. A. Krasnov. On the volume formula for hyperbolic $4$-dimensional simplex. Contemporary Mathematics. Fundamental Directions, Differential and functional differential equations, Tome 63 (2017) no. 3, pp. 494-503. http://geodesic.mathdoc.fr/item/CMFD_2017_63_3_a6/