Fibonacci anyons for the representations of the $SU(2)^5_q$ symmetry in context of topological phases of matter and quantum computing field of researches. In this language the $A_{v}=W_{\triangle_{1}}^{5}(j_{lv})$ building block amplitude is just the known F symbol that appears in those anyonic models [@ZhenghanWang; @Pachos]. The partition function is about gluing these $A_{v}$ amplitudes, which makes sense from the point of view of quantum computation. An important result in the field of quantum computation is that a higher dimensional Hilbert space can be decomposed into a network of qubits and 2-level quantum gates [@nielsen_chuang], and that with at least 3 Fibonacci anyon representations, one can implement the qubits, where the braids of these anyons can approximate any 2-level quantum gate, making Fibonacci anyons a sufficient substrate for universal quantum computation [@ZhenghanWang]. So $Z_{q}(nj)$ of $n$ “anyon states”, for large $n$, is a topological quantum liquid or a topological quantum computer but described by the network of the building block amplitudes $A_{v}=W_{\triangle_{1}}^{5}(j_{lv})$. We note that the dual 2-complex of the quantum tetrahedron is made of one vertex in the bulk and 4 nodes on the triangular boundary faces of the triangulation. So in fact the quantum tetrahedron carries 4 anyonic charges, the 