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The hyperbolic space $\mathbb H3$, \mathbb{H}^3$, has a boundary $\mathbb CP1$.\mathbb{CP}^1$. A ideal tetrahedron in $\mathbb H3$, \mathbb{H}^3$, is a tetrahedron, where the four vertices are on the boundary $\mathbb CP1$. \mathbb{CP}^1$. The four vertices of the tetrahedron may be parametrized by four complex numbers $z1, z2z_1, z_2, z3z_3, z4$z_4$. What is the surface of this ideal tetrahedron, as function of $z1, z2z_1, z_2, z3z_3, z4$ z_4$?. |
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Surface of a Ideal Tetrahedron in Hyperbolic Space H3The 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 $z1, z2, z3, z4$ ?.
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