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A classical 6j–symbol is a real number which can be associated to a
labelling of the six edges of a tetrahedron by irreducible representations
of SU(2). This abstract association is traditionally used simply to
express the symmetry of the 6j–symbol, which is a purely algebraic
object; however, it has a deeper geometric significance. Ponzano and
Regge, expanding on work of Wigner, gave a striking (but unproved)
asymptotic formula relating the value of the 6j–symbol, when the
dimensions of the representations are large, to the volume of an honest
Euclidean tetrahedron whose edge lengths are these dimensions. The goal
of this paper is to prove and explain this formula by using geometric
quantization. A surprising spin-off is that a generic Euclidean
tetrahedron gives rise to a family of twelve scissors-congruent but
non-congruent tetrahedra.
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