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We propose a quantum version of the quadratic volume simplicity constraintfor the EPRL spin foam model. It relies on a formula for the volume of4-dimensional polyhedra, depending on its bivectors and the knotting class ofits boundary graph. While this leads to no further condition for the 4-simplex,the constraint becomes non-trivial for more complicated boundary graphs. Weshow that, in the semi-classical limit of the hypercuboidal graph, theconstraint turns into the geometricity condition observed recently by severalauthors.

On the volume simplicity constraint in the EPRL spin foam model