  We revisit the the large spin asymptotics of 15j symbols in terms of cosines
of the 4d Euclidean Regge action, as derived by Barrett and collaborators using
a saddle point approximation. We bring it closer to the perspective of
area-angle Regge calculus and twisted geometries, and compute explicitly the
Hessian and phase offsets. We then extend it to more general SU(2) graph
invariants, showing that saddle points still exist and have a similar
structure. For graphs dual to 4d polytopes we find again two distinct saddle
points leading to a cosine asymptotic formula, however a conformal
shape-mismatch is allowed by these configurations, and the asymptotic action is
thus a generalisation of the Regge action. The allowed mismatch correspond to
angle-matched twisted geometries, 3d polyhedral tessellations with adjacent
faces matching areas and 2d angles, but not their diagonals. We study these
geometries, identify the relevant subsets corresponding to 3d Regge data and
flat polytope data, and discuss the corresponding Regge actions emerging in the
asymptotics. Finally, we also provide the first numerical confirmation of the
large spin asymptotics of the 15j symbol. We show that the agreement is
accurate to the per cent level already at spins of order 10, and the
next-to-leading order oscillates with the same frequency and same global phase.
