  We report neutron-diffraction results on single-crystal CaMn$_2$P$_2$
containing corrugated Mn honeycomb layers and determine its ground-state
magnetic structure. The diffraction patterns consist of prominent (1/6, 1/6,
$L$) reciprocal lattice unit (r.l.u.; $L$ = integer) magnetic Bragg
reflections, whose temperature-dependent intensities are consistent with a
first-order antiferromagnetic phase transition at the N\'eel temperature
$T_{\rm N} = 70(1)$ K. Our analysis of the diffraction patterns reveals an
in-plane $6\times6$ magnetic unit cell with ordered spins that in the
principal-axis directions rotate by 60-degree steps between nearest neighbors
on each sublattice that forms the honeycomb structure, consistent with the
$P_Ac$ magnetic space group. We find that a few other magnetic subgroup
symmetries ($P_A2/c$, $P_C2/m$, $P_S\bar{1}, P_C2, P_Cm, P_S1$) of the
paramagnetic $P\bar{3}m11^\prime$ crystal symmetry are consistent with the
observed diffraction pattern. We relate our findings to frustrated
$J_1$-$J_2$-$J_3$ Heisenberg honeycomb antiferromagnets with single-ion
anisotropy and the emergence of Potts nematicity
