the reciprocal of a Simple Hexagonal Bravais lattice with lattice constants a, b, and c (|a|=|b| =a, and |c|=c ) and α=β=90˚ and γ = 120˚ is another Simple Hexagonal lattice with lattice constants a*, b*, and c* where |c*| =c* 1/c  and |a*| = |b*|=a*  , and wherein α*=β*=90˚ and γ* = 60˚, and a* is oriented at an angle of 30˚ with respect to a, b* is perpendicular to a, and c* is parallel to c while both c and c* are perpendicular to a, b,  a*, and b*,

Calculate a, b, c, a*, b* and c* on an (001) stereographic projection