Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 4D-Polytopes and Their Dual Polytopes of the Coxeter Group $W(A_{4})$
  Represented by Quaternions   4-dimensional $A_{4}$ polytopes and their dual polytopes have been
constructed as the orbits of the Coxeter-Weyl group $W(A_{4})$ where the group
elements and the vertices of the polytopes are represented by quaternions.
Projection of an arbitrary $W(A_{4})$ orbit into three dimensions is made using
the subgroup $W(A_{3})$. A generalization of the Catalan solids for 3D
polyhedra has been developed and dual polytopes of the uniform $A_{4}$
polytopes have been constructed.

16
The categories of this paper are: stat
21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat