Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On a triply periodic polyhedral surface whose vertices are Weierstrass
  points   In this paper, we will construct an example of a closed Riemann surface $X$
that can be realized as a quotient of a triply periodic polyhedral surface $\Pi
\subset \mathbb{R}^3$ where the Weierstrass points of $X$ coincide with the
vertices of $\Pi.$ First we construct $\Pi$ by attaching Platonic solids in a
periodic manner and consider the surface of this solid. Due to periodicity we
can find a compact quotient of this surface, which has genus $g = 3.$ We claim
that the resulting surface is not hyperelliptic and also that it is regular. By
regular, we mean that the automorphism group of $X$ is transitive on flags. The
symmetries of $X$ allow us to construct hyperbolic structures and various
translation structures on $X$ that are compatible with its conformal type. The
translation structures are the geometric representations of the holomorphic
1-forms of $X,$ which allow us to identify the Weierstrass points.

37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
21
The categories of this paper are: adap-org