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    "# Voronoi tessellation to identify local structures"
   ]
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    "Voronoi tessellation can be used for identification of local structure\n",
    "by counting the number of faces of the Voronoi polyhedra of an\n",
    "atom {cite}`Finney1970,Tanemura1977`. For each atom a vector $\\langle n_3~n_4~n_5~n_6 \\rangle$\n",
    "can be calculated where $n_3$ is the number of Voronoi faces of the\n",
    "associated Voronoi polyhedron with three vertices, $n_4$ is with four\n",
    "vertices and so on. Each perfect crystal structure such as a signature\n",
    "vector, for example, bcc can be identified by $\\langle 0~6~0~8 \\rangle$\n",
    "and fcc can be identified using $\\langle 0~12~0~0 \\rangle$. It is also a\n",
    "useful tool for identifying icosahedral structure which has the\n",
    "fingerprint $\\langle 0~0~12~0 \\rangle$. In pyscal, the voronoi vector\n",
    "can be calculated using,\n",
    "\n",
    "``` python\n",
    "import pyscal.core as pc\n",
    "sys = pc.System()\n",
    "sys.read_inputfile('conf.dump')\n",
    "sys.find_neighbors(method='voronoi')\n",
    "sys.calculate_vorovector()\n",
    "```\n",
    "\n",
    "The vector for each atom can be accessed using\n",
    "[Atom.vorovector](https://docs.pyscal.org/en/latest/pyscal.html#pyscal.catom.Atom.vorovector).\n",
    "Furthermore, the associated Voronoi volume of the polyhedron, which may\n",
    "be indicative of the local structure, is also automatically calculated\n",
    "when finding neighbors using\n",
    "[System.find_neighbors](https://docs.pyscal.org/en/latest/pyscal.html#pyscal.core.System.find_neighbors).\n",
    "This value for each atom can be accessed by\n",
    "[Atom.volume](https://docs.pyscal.org/en/latest/pyscal.html#pyscal.catom.Atom.volume). An averaged\n",
    "version of the volume, which is averaged over the neighbors of an atom\n",
    "can be accessed using [Atom.avg_volume](https://docs.pyscal.org/en/latest/pyscal.html#pyscal.catom.Atom.avg_volume).\n",
    "\n",
    "\n",
    "## References\n",
    "\n",
    "```{bibliography} ../references.bib\n",
    ":filter: docname in docnames\n",
    ":style: unsrt\n",
    "```"
   ]
  }
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