A closed form expression for multiplicity-free quantum 6-j symbols (MFS) was proposed in [1] for symmetric representations of $U_q(s{l}_N)$, which are the simplest class of multiplicity-free representations. In this paper we rewrite this expression in terms of q-hypergeometric series ${}_4\mathrm{\Phi }_3$. We claim that it is possible to express any MFS through the 6-j symbol for $U_q(s{l}_2)$ with a certain factor. It gives us a universal tool for the extension of various properties of the quantum 6-j symbols for $U_q(s{l}_2)$ to the MFS. We demonstrate this idea by deriving the asymptotics of the MFS in terms of associated tetrahedron for classical algebra $U(s{l}_N)$.

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 $N=2$.

[1]中提出了无重数量子6-j符号（MFS）的闭式表达式，用于对称表示。 ${ü}_q（s{升}_{ñ}）$，这是无重表示形式中最简单的一类。在本文中，我们根据q超几何级数重写了此表达式${}_4\mathrm{\Phi }_3$。我们声称可以通过6-j符号来表示任何MFS${ü}_q（s{升}_2）$有一定的因素。它为我们提供了扩展量子6-j符号各种特性的通用工具，${ü}_q（s{升}_2）$到MFS。我们通过用经典代数的相关四面体派生MFS的渐近性来证明这一思想$ü（s{升}_{ñ}）$。

接下来，我们使用已知的超几何恒等式（例如参数排列和Sears变换）研究MFS对称性。我们描述了MFS的对称组。结果，我们得到了新的对称性，它们是四面体对称性和Regge对称性的推广。$ñ=2$。