Single crystal EPR spectra of K12[As2W18O66Cu3(H2O)2]${cdot}$11H2O exhibit an orientation-dependent fine structure of an S = 3/2 system which is accounted for by the exchange and magnetic dipole interactions among the three Cu2+ ions. The hyperfine structure and the lines from the S = 1/2 manifolds have not been observed. The isotropic exchange parameters determined from the magnetic susceptibility data at 5-300 K are J1 = J2 =-7.8 cm-1. The magnitude of J values suggests that the unpaired electrons on three Cu2+ ions interact through a sequence of six bonds involving two tungsten atoms and three oxygen atoms. The Cu-Cu distance, 4.37 $AA$, determined from the EPR spectra is considerably smaller than the value from the X-ray crystal structure determination, 4.76 $pm$ 0.03 $AA$, indicating that the point-dipole model underestimates the dipolar interaction.