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JOURNALS // Siberian Journal of Pure and Applied Mathematics // Archive

Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 2005 Volume 5, Issue 4, Pages 14–31 (Mi vngu217)

Prisms in $H^3$

D. A. Derevnin


Abstract: Main result of this work is a formula for calculation of volume of compact quadrangular prism of special type. We prove that any acute prism in $H^3$ can be divided into finite number of given type. So, it gives an algorithm to find volume of arbitrary $n$-angled prism in $H^3$ with dihedral angles less than $\pi/2$. Also, we state the full classification of quadrangular Coxeter prisms in $H^3$. In addendum, there are all 30 Coxeter schemes, corresponding to quadrangular prisms and their hyperbolic volumes.

UDC: 514.13+514.132



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