The hyperbolic space $\mathbb{H}^3$, has a boundary $\mathbb{CP}^1$.


A ideal tetrahedron in $\mathbb{H}^3$, is a tetrahedron, where the four vertices are on the boundary $\mathbb{CP}^1$. 


The four vertices of the tetrahedron may be parametrized by four complex numbers $z\_1, z\_2, z\_3, z\_4$.


What is the surface of this ideal tetrahedron, as function of $z\_1, z\_2, z\_3, z\_4$?



Surface of a Ideal Tetrahedron in Hyperbolic Space H3
The answer is $4\pi.$


