  The Avogadro constant links the atomic and the macroscopic properties of
matter. Since the molar Planck constant is well known via the measurement of
the Rydberg constant, it is also closely related to the Planck constant. In
addition, its accurate determination is of paramount importance for a
definition of the kilogram in terms of a fundamental constant. We describe a
new approach for its determination by "counting" the atoms in 1 kg
single-crystal spheres, which are highly enriched with the 28Si isotope. It
enabled isotope dilution mass spectroscopy to determine the molar mass of the
silicon crystal with unprecedented accuracy. The value obtained, 6.02214084(18)
x 10^23 mol^-1, is the most accurate input datum for a new definition of the
kilogram.
