The reciprocal to a simple hexagonal Bravais lattice with lattice constants a and c is another simple hexagonal lattice with lattice constants 2 π π / c and 4 π π / ( a 3 ) rotated through 90° about the c axis with respect to the direct lattice. The simple hexagonal lattice is therefore said to be self-dual, having the same symmetry in reciprocal space as in real space. Primitive translation vectors for this simple hexagonal Bravais lattice vectors are a 1 = 3 2 a x ^ ^ + 1 2 a y ^ ^ , a 2 = − − 3 2 a x ^ ^ + 1 2 a y ^ ^ , a 3 = c z ^ ^ .