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What are the software tools (if possible open source) or methods we can use for constructing a nanocluster, most preferably with high symmetry such as icosahedron, octahedron, cuboctahedron etc. ?

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A possible tool is the ASE python package (open-source):

https://wiki.fysik.dtu.dk/ase/ase/cluster/cluster.html

Another tool is materials studio software. Unfortunately, it is not free.

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Nanocut

From its site:

Nanocut is a program designed to cut out various objects from three dimensional crystal structures. It is aimed to be helpful when creating geometry input for atomistic simulations. Currently it can create following objects:

  • Spherical cluster
  • Polyhedral cluster
  • Cylindrical cluster
  • Spherical wire (1D periodic)
  • Polyhedral wire (1D periodic)
  • Plain slab (2D periodic)
  • Supercells (3D periodic)
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Atomsk

I like to use Atomsk to build clusters.

Atomsk is a free, Open Source command-line program dedicated to the creation, manipulation, and conversion of data files for atomic-scale simulations. It supports the file formats used by many programs.

Atomsk proposes options for applying elementary transformations: duplicate, rotate, deform, insert dislocations, merge several systems, create bicrystals and polycrystals, etc. These elementary tools can be combined to construct and shape a wide variety of atomic systems. To learn more, you are invited to read the documentation, and to follow the tutorials.

"Atomsk: A tool for manipulating and converting atomic data files" Pierre Hirel, Comput. Phys. Comm. 197 (2015) 212-219 doi:10.1016/j.cpc.2015.07.012

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