  In this article we consider specific bivector geometries which arise in the
large-spin limit of the extension of the Engle-Pereira-Rovelli-Livine spin foam
model for quantum gravity by Kaminski, Kisielowski and Lewandowski. We address
the implementation of volume simplicity constraints, which are required to
ensure that a $4d$ metric can be reconstructed from the bivector geometry. We
find that the necessary conditions are closely related, but not quite equal to
the Hopf link volume simplicity constraints introduced in earlier works. We
estimate the number of independent geometricity conditions for arbitrary
bivector geometries, and find that they always agree with the number of Hopf
links on the graph minus one, suggesting that the geometricity conditions can
generically be formulated by deformation of the Hopf link volume simplicity
constraints.
