  Further investigation of the participant plane correlations within a Glauber
model framework is presented, focusing on correlations between three or four
participant planes of different order. A strong correlation is observed for
$\cos(2\Phi_{2}^*+3\Phi_{3}^*-5\Phi_{5}^*)$ which is a reflection of the
elliptic shape of the overlap region. The correlation between the corresponding
experimental reaction plane angles can be easily measured. Strong correlations
of similar geometric origin are also observed for
$\cos(2\Phi_{2}^*+4\Phi_{4}^*-6\Phi_{6}^*)$,
$\cos(2\Phi_2^*-3\Phi_3^*-4\Phi_4^*+5\Phi_5^*)$,
$\cos(6\Phi_2^*+3\Phi_3^*-4\Phi_4^*-5\Phi_5^*)$,
$\cos(\Phi_1^*-2\Phi_2^*-3\Phi_3^*+4\Phi_4^*)$,
$\cos(\Phi_1^*+6\Phi_2^*-3\Phi_3^*-4\Phi_4^*)$, and
$\cos(\Phi_1^*+2\Phi_2^*+3\Phi_3^*-6\Phi_6^*)$, which are also measurable.
Experimental measurements of the corresponding reaction plane correlators in
heavy ion collisions at RHIC and the LHC may improve our understanding of the
physics underlying the measured higher order flow harmonics.
