  We conjecture an upper bound on the growth of the Yokota invariant of
polyhedral graphs, extending a previous result on the growth of the
$6j$-symbol. Using Barrett's Fourier transform we are able to prove this
conjecture in a large family of examples. As a consequence of this result, we
prove the Turaev-Viro Volume Conjecture for a new infinite family of hyperbolic
manifolds.
