The space of shapes of a tetrahedron with fixed face areas is naturally a symplectic manifold of real dimension two. This symplectic manifold turns out to be a Kahler manifold and can be parametrized by a single complex coordinate

given by the cross ratio of four complex numbers obtained by stereographically projecting the unit face normals onto the complex plane. This Demonstration illustrates how this works in the simplest case of a tetrahedron

whose four face areas are equal. For convenience, the cross-ratio coordinate

is shifted and rescaled to

so that the regular tetrahedron corresponds to

, in which case the upper half-plane is mapped conformally into the unit disc

. The equi-area tetrahedron

is then drawn as a function of the unit disc coordinate

.