Reciprocal of the reciprocal lattice is the original lattice

[girlinphysics]

In my course we are currently studyinh Bravis lattices. We were told that the reciprocal of the reciprocal lattice is the original lattice. This is very easy to prove when given an example of a SC/BCC/FCC lattice, however, is there a formal proof for this?

 

[DrDu]

In my course we are currently studyinh Bravis lattices. We were told that the reciprocal of the reciprocal lattice is the original lattice. This is very easy to prove when given an example of a SC/BCC/FCC lattice, however, is there a formal proof for this?

I suppose it is straight forward. Did you try to proove it yourself?