# Voronoi tessellation to identify local structures¶

Voronoi tessellation can be used for identification of local structure by counting the number of faces of the Voronoi polyhedra of an atom {cite}Finney1970,Tanemura1977. For each atom a vector $$\langle n_3~n_4~n_5~n_6 \rangle$$ can be calculated where $$n_3$$ is the number of Voronoi faces of the associated Voronoi polyhedron with three vertices, $$n_4$$ is with four vertices and so on. Each perfect crystal structure such as a signature vector, for example, bcc can be identified by $$\langle 0~6~0~8 \rangle$$ and fcc can be identified using $$\langle 0~12~0~0 \rangle$$. It is also a useful tool for identifying icosahedral structure which has the fingerprint $$\langle 0~0~12~0 \rangle$$. In pyscal, the voronoi vector can be calculated using,

import pyscal.core as pc
sys = pc.System()

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