  Recently Waegell and Aravind [J. Phys. A: Math. Theor. 45 (2012), 405301, 13
pages] have given a number of distinct sets of three-qubit observables, each
furnishing a proof of the Kochen-Specker theorem. Here it is demonstrated that
two of these sets/configurations, namely the $18_{2} - 12_{3}$ and $2_{4}14_{2}
- 4_{3}6_{4}$ ones, can uniquely be extended into geometric hyperplanes of the
split Cayley hexagon of order two, namely into those of types ${\cal
V}_{22}(37; 0, 12, 15, 10)$ and ${\cal V}_{4}(49; 0, 0, 21, 28)$ in the
classification of Frohardt and Johnson [Comm. Algebra 22 (1994), 773-797].
Moreover, employing an automorphism of order seven of the hexagon, six more
replicas of either of the two configurations are obtained.
