  We study the BPS invariants of the preferred Calabi-Yau resolution of ADE
polyhedral singularities C^3/G given by Nakamura's G-Hilbert schemes. Genus 0
BPS invariants are defined by means of the moduli space of torsion sheaves as
proposed by Sheldon Katz. We show that these invariants are equal to half the
number of certain positive roots of an ADE root system associated to G. This is
in agreement with the prediction via Gromov-Witten theory.
