We present band structure calculations and quantum oscillation measurements on LuRh2Si2, which is an ideal reference to the intensively studied quantum critical heavy-fermion system YbRh2Si2. Our band structure calculations show a strong sensitivity of the Fermi surface on the position of the silicon atoms zSi within the unit cell. Single crystal structure refinement and comparison of predicted and observed quantum oscillation frequencies and masses yield zSi = 0.379 c in good agreement with numerical lattice relaxation.