Recent work on state sum models of quantum gravity in 3 and 4 dimensions has led to interest in the 'quantum tetrahedron'. Starting with a classical phase space whose points correspond to geometries of the tetrahedron in M 3 , we use geometric quantization to obtain a Hilbert space of states. This Hilbert space has a basis of states labeled by the areas of the faces of the tetrahedron together with one more quantum number,
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Baez et al. (1999) studied this question.
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