2
$\begingroup$

In this question : Two Fundamental Polygons for the Double Torus?

Lee Mosher says

There are four octagon gluing patterns (up to rotation and relabelling) which give a double torus.

It is a very interesting result to me, which makes me think about the following question.

How may patterns (up to rotation and relabelling) to glue a $4n$-gon to a genus $n$ surface?

I tried to find all above patterns for a $12$-gon and I failed, since there are too many possibilities.

I feel like my problem is a natural one, so I'd love to know if it's already been solved.

$\endgroup$
2
  • $\begingroup$ Possibly relevant: oeis.org/A291371. (I don't know what a chord diagram is, just went through OEIS entries that have the word genus and start 1, 4, ...) $\endgroup$
    – ronno
    Commented Sep 6, 2023 at 11:49
  • $\begingroup$ @ronno Thank you so much. That is exactly what I want to know. I also want to thank you for letting me know about this interesting website OEIS. $\endgroup$
    – knock kncok
    Commented Sep 7, 2023 at 2:49

0

Reset to default

You must log in to answer this question.