The hyperbolic space $\mathbb H3$, has a boundary $\mathbb CP1$.
A ideal tetrahedron in $\mathbb H3$, is a tetrahedron, where the four vertices are on the boundary $\mathbb CP1$.
The four vertices of the tetrahedron may be parametrized by four complex $z1, z2, z3, z4$
What is the surface of this ideal tetrahedron, as function of $z1, z2, z3, z4$ ?.
Answer from Igor Rivin (http://mathoverflow.net/users/11142/igor-rivin) :
The answer is $4 \pi$
The surface of a tetrahedron is the union of four ideal triangles, all of which have area π.