I need the explicit quantum 6j symbols for the Haagerup fusion category for a physics research project. This paper math/9803044 by Asaeda and Haagerup brute-force constructs the Haagerup subfactor, by giving explicit connections on four graphs. So I wonder: (1) Is the data of connections equivalent to the quantum 6j symbols? (2) If so, how can I translate?

Any help or direction to references is very much appreciated!