Understanding the Reciprocal Lattice Structure of Zinc-Blende

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What is the reciprocal lattice structure of the zinc-blende structure?
 
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zinc-blende structure is FCC; reciprocal lattice structure is BCC
 
But I though zinc-blende was not simply FCC but FCC with a basis. Or as I like to think of it , as two interlocking FCC lattices. So are you saying the reciprocal lattice is two interlocking BCC lattices?
 

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