We use photoluminescence spectroscopy of bright and dark exciton states in single InP/GaInP quantum dots to measure hyperfine interaction of the valence band hole with nuclear spins polarized along the sample growth axis. The ratio of the hyperfine c
onstants for the hole (C) and electron (A) is found to be C/A~-0.11. In InP dots the contribution of spin 1/2 phosphorus nuclei to the hole-nuclear interaction is weak, which enables us to determine experimentally the value of C for spin 9/2 indium nuclei as C_In~-5 micro-eV. This high value of C is in good agreement with recent theoretical predictions and suggests that the hole-nuclear spin interaction has to be taken into account when considering spin qubits based on holes.
