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ZnS has a ccp structure with S2- ions forming FCC lattice with Zn2+ ions at half the tetrahedral voids

Attached is a table showing no. of nearest neighbours and their distance for an S2- ion

'a' is edge length of the unit cell

I want to know how the distance to the 3rd & 5th nearest ion is √11a/4 & √19a/11, i.e how to prove this.

Thanks ... any help is appreciated

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# Distance to 3rd and 5th nearest ion to S2- in ZnS structure

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