  A closed form expression for multiplicity-free quantum 6-j symbols (MFS) was
proposed in arXiv:1302.5143 for symmetric representations of $U_q(sl_N)$, which
are the simplest class of multiplicity-free representations. In this paper we
rewrite this expression in terms of q-hypergeometric series ${}_4\Phi_3$. We
claim that it is possible to express any MFS through the 6-j symbol for
$U_q(sl_2)$ with a certain factor. It gives us a universal tool for the
extension of various properties of the quantum 6-j symbols for $U_q(sl_2)$ to
the MFS. We demonstrate this idea by deriving the asymptotics of the MFS in
terms of associated tetrahedron for classical algebra $U(sl_N)$.
  Next we study MFS symmetries using known hypergeometric identities such as
argument permutations and Sears' transformation. We describe symmetry groups of
MFS. As a result we get new symmetries, which are a generalization of the
tetrahedral symmetries and the Regge symmetries for N = 2.
