Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A toolkit for the construction of icosahedral particles with local
  symmetry axes   A formalism is developed which allows to determine the locations of all local
symmetry axes of three-dimensional particles with overall icosahedral symmetry.
It relies on the fact that the root system of the non-crystallographic Coxeter
group H_3 encodes the locations of the planes of reflection that generate the
discrete rotational symmetries of the particles. Via an appropriate extension
of the root system, new planes of reflection are introduced which determine
local axes of rotational symmetry. An easy-to-implement formalism is derived
that allows to compute the surface structure of any three-dimensional
icosahedral particle with local symmetries. It can be used also for particles
with overall octahedral and tetrahedral symmetry in conjunction with the root
systems of the corresponding reflection groups.
  Applications to viruses are discussed explicitly. It is shown that the
concept of quasi-equivalence in Caspar-Klug Theory corresponds to the special
case of local six-fold symmetry axes contained in the theory developed here,
and the corresponding geometries can hence be obtained with this formalism
based on the root system of H_3.
  Moreover, as a by-product, the theory answers the long-standing open question
why only certain types of capsomeres, i.e. clusters of protein subunits, are
observed in the surface structures of viruses. Since the types of the
capsomeres are determined by the orders of the local symmetry axes on which
they are located, the possible types of capsomeres are restricted by the
spectrum of local symmetry axes allowed by the theory. Based on this we
determine the spectrum of all capsomere types that may occur in viral capsids
and give explicit examples for the lower-order cases.

24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat