Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Geometric realizations of regular abstract polyhedra with automorphism
  group $H_3$   A \textit{geometric realization} of an abstract polyhedron $\mathcal{P}$ is a
mapping $\rho : \mathcal{P} \to \mathbb{E}^3$ that sends an $i$-face to an open
set of dimension $i$. This work adapts a method based on Wythoff construction
to generate a full rank realization of a regular abstract polyhedron from its
automorphism group $\Gamma$. The method entails finding a real orthogonal
representation of $\Gamma$ of degree 3 and applying its image to suitably
chosen open sets in space. To demonstrate the use of the method, we apply it to
the abstract polyhedra whose automorphism groups are isomorphic to the
non-crystallographic Coxeter group $H_3$.

1
The categories of this paper are: cs
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con