I'm genuinely curious: What about this graph makes it interesting?

Its relation to the j-invariant, modular forms, Steiner System (5,8,24), Binary Golay Code G24, Mathieu Group M24, the Leech Lattice, the Monster Group, Monstrous Moonshine, and the Miracle Octad Generator...

[1] https://en.wikipedia.org/wiki/J-invariant

[2] https://en.wikipedia.org/wiki/Steiner_system

[3] https://en.wikipedia.org/wiki/Binary_Golay_code

[4] https://en.wikipedia.org/wiki/Mathieu_group_M24

[5] https://en.wikipedia.org/wiki/Leech_lattice

[6] https://en.wikipedia.org/wiki/Monster_group

[7] https://en.wikipedia.org/wiki/Monstrous_moonshine

[8] https://en.wikipedia.org/wiki/Miracle_Octad_Generator

http://finitegeometry.org/sc/24/MOG.html