schläfli formula
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2021 ◽  
Vol 21 (1) ◽  
pp. 279-315
Author(s):  
Filippo Mazzoli
Keyword(s):  

2019 ◽  
Vol 51 (5) ◽  
pp. 765-775
Author(s):  
Arseniy Akopyan ◽  
Ivan Izmestiev

2016 ◽  
Vol 25 (06) ◽  
pp. 1650030 ◽  
Author(s):  
Ji-Young Ham ◽  
Joongul Lee

Let [Formula: see text] be the family of two bridge knots of slope [Formula: see text]. We calculate the volumes of the [Formula: see text] cone-manifolds using the Schläfli formula. We present the concrete and explicit formula of them. We apply the general instructions of Hilden, Lozano and Montesinos-Amilibia and extend the Ham, Mednykh and Petrov’s methods. As an application, we give the volumes of the cyclic coverings over those knots. For the fundamental group of [Formula: see text], we take and tailor Hoste and Shanahan’s. As a byproduct, we give an affirmative answer for their question whether their presentation is actually derived from Schubert’s canonical two-bridge diagram or not.


2014 ◽  
Vol 23 (12) ◽  
pp. 1450064 ◽  
Author(s):  
Ji-Young Ham ◽  
Alexander Mednykh ◽  
Vladimir Petrov

We calculate the volumes of the hyperbolic twist knot cone-manifolds using the Schläfli formula. Even though general ideas for calculating the volumes of cone-manifolds are around, since there is no concrete calculation written, we present here the concrete calculations. We express the length of the singular locus in terms of the distance between the two axes fixed by two generators. In this way the calculation becomes easier than using the singular locus directly. The volumes of the hyperbolic twist knot cone-manifolds simpler than Stevedore's knot are known. As an application, we give the volumes of the cyclic coverings over the hyperbolic twist knots.


2008 ◽  
Vol 10 (supp01) ◽  
pp. 835-842 ◽  
Author(s):  
FENG LUO

Several identities similar to the Schläfli formula are established for tetrahedra in a space of constant curvature.


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