Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nested polyhedra and indices of orbits of Coxeter groups of
  non-crystallographic type   The invariants of finite-dimensional representations of simple Lie algebras,
such as even-degree indices and anomaly numbers, are considered in the context
of the non-crystallographic finite reflection groups $H_2$, $H_3$ and $H_4$.
Using a representation-orbit replacement, the definitions and properties of the
indices are formulated for individual orbits of the examined groups. The
indices of orders two and four of the tensor product of $k$ orbits are
determined. Using the branching rules for the non-crystallographic Coxeter
groups, the embedding index is defined similarly to the Dynkin index of a
representation. Moreover, since the definition of the indices can be applied to
any orbit of non-crystallographic type, the algorithm allowing to search for
the orbits of smaller radii contained within any considered one is presented
for the Coxeter groups $H_2$ and $H_3$. The geometrical structures of nested
polytopes are exemplified.

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The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
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The categories of this paper are: solv-int
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The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
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The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex