  We show that a new symmetry requirement on the GFT field, in the context of
an extended GFT formalism, involving both Lie algebra and group elements,
leads, in 3d, to Feynman amplitudes with a simplicial path integral form based
on the Regge action, to a proper relation between the discrete connection and
the triad vectors appearing in it, and to a much more satisfactory and
transparent encoding of simplicial geometry already at the level of the GFT
action.
