# Volume of a spherical tetrahedron

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 ?

• 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). – hardmath Dec 14 '13 at 14:16
• From the abstract spherical tetrahedron, which is in a $3$-dimensional spherical space of constant curvature $+1$ – Sigur Dec 14 '13 at 14:50
• What exactly is it you want to know? – Igor Rivin Dec 14 '13 at 15:34
• What is $q_0$, $q_1$, $q_2$ and $z_0$ would be a good start ... thank you Sigur for sorting the link. – Herman Dec 14 '13 at 15:38