It's also really similar to something that music theorists do. In the 19th century, Hugo Riemann came up with a way of graphing chord relationships and note relationships using transformations and the properties of the tonal system. He called them tonnetz and people make 3D graphs today in a similar way to the change-ringing graphs.
Look at this shit:
http://www-rcf.usc.edu/~echew/papers/CiM2003/ec-cim2003.pdf