scholarly journals Erratum to: Volume of a doubly truncated hyperbolic tetrahedron

2014 ◽  
Vol 88 (1-2) ◽  
pp. 199-200 ◽  
Author(s):  
Alexander Kolpakov ◽  
Jun Murakami
Keyword(s):  
Hyperbolic Tetrahedron

scholarly journals Explicit volume formula for a hyperbolic tetrahedron in terms of edge lengths

2021 ◽  
Author(s):  
Nikolay Abrosimov ◽  
Bao Vuong
Keyword(s):  
Convex Hull ◽  
Hyperbolic Space ◽  
General Type ◽  
Integral Formula ◽  
Sufficient Conditions ◽  
Gram Matrix ◽  
Dihedral Angles ◽  
Hyperbolic Tetrahedron ◽  
Volume Formula ◽  
Necessary And Sufficient

We consider a compact hyperbolic tetrahedron of a general type. It is a convex hull of four points called vertices in the hyperbolic space [Formula: see text]. It can be determined by the set of six edge lengths up to isometry. For further considerations, we use the notion of edge matrix of the tetrahedron formed by hyperbolic cosines of its edge lengths. We establish necessary and sufficient conditions for the existence of a tetrahedron in [Formula: see text]. Then we find relations between their dihedral angles and edge lengths in the form of a cosine rule. Finally, we obtain exact integral formula expressing the volume of a hyperbolic tetrahedron in terms of the edge lengths. The latter volume formula can be regarded as a new version of classical Sforza’s formula for the volume of a tetrahedron but in terms of the edge matrix instead of the Gram matrix.

scholarly journals Elementary formulas for a hyperbolic tetrahedron

2006 ◽  
Vol 47 (4) ◽  
pp. 687-695 ◽  
Author(s):  
A. D. Mednykh ◽  
M. G. Pashkevich
Keyword(s):  
Hyperbolic Tetrahedron

scholarly journals The Dual Jacobian of a Generalised Hyperbolic Tetrahedron, and Volumes of Prisms

2016 ◽  
Vol 39 (1) ◽  
pp. 45-67 ◽  
Author(s):  
Alexander KOLPAKOV ◽  
Jun MURAKAMI
Keyword(s):  
Hyperbolic Tetrahedron

scholarly journals Volume of a doubly truncated hyperbolic tetrahedron

2012 ◽  
Vol 85 (3) ◽  
pp. 449-463 ◽  
Author(s):  
Alexander Kolpakov ◽  
Jun Murakami
Keyword(s):  
Hyperbolic Tetrahedron
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