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In the paper Jun Murakami, The volume formulas for a spherical tetrahedron a formula for the volume of a spherical tetrahedron is given. I am trying to work through the details for the specific example where the dihedral angles are $\theta_1=\pi/4$, $\theta_2=\pi/4$, $\theta_3=\pi/4$, $\theta_4=\pi/6$, $\theta_5=\pi/6$ and $\theta_6=\pi/6$. I get lost in a sea of root threes. Could someone help ?

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  • $\begingroup$ While "spherical triangle" has a clear meaning (at least when three points are given within the same hemisphere of a sphere), I'm not certain what "spherical tetrahedron" should mean. Four points on a sphere might be considered to "enclose" the entire sphere, for example (and give a spherical volume). $\endgroup$ – hardmath Dec 14 '13 at 14:16
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    $\begingroup$ From the abstract spherical tetrahedron, which is in a $3$-dimensional spherical space of constant curvature $+1$ $\endgroup$ – Sigur Dec 14 '13 at 14:50
  • $\begingroup$ What exactly is it you want to know? $\endgroup$ – Igor Rivin Dec 14 '13 at 15:34
  • $\begingroup$ What is $q_0$, $q_1$, $q_2$ and $z_0$ would be a good start ... thank you Sigur for sorting the link. $\endgroup$ – Herman Dec 14 '13 at 15:38

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