Having that shape become more important to a civilisation than the circle because it has something to do with the geometry of hyperspace seems like it could be an interesting conceit for a sci-fi setting.
Learning how to expand e.g. 3/7 into 1/n + 1/m + ... using their methods was a fascinating experience.
I wouldn't want to suffer under such constraints day to day but it was one of the most memorable parts of the History of Mathematics course I took alongside what was other a mostly pure maths degree.
Second thought would probably be Derek Künsken. (no claim he's necessarily the second best option but he's definitely the second author I've read recently enough to have the name of in brain cache to come to mind as "could almost certainly pull it off")
It's not aliens but humans, and it's not an 8-loop geometry, but without spoiling it too much it's safe to say that discovering how hyperspace works is the central concept guiding the story.
Sounds like at least £2.99's worth of fun to me from the blurb, so it's now queued up.
I swear I'll get to it eventually.
... honest.