  Disregarding the identity, the remaining 63 elements of the generalized
three-qubit Pauli group are found to contain 12096 distinct copies of Mermin's
magic pentagram. Remarkably, 12096 is also the number of automorphisms of the
smallest split Cayley hexagon. We give a few solid arguments showing that this
may not be a mere coincidence. These arguments are mainly tied to the structure
of certain types of geometric hyperplanes of the hexagon. It is further
demonstrated that also an (18_{2}, 12_{3})-type of magic configurations,
recently proposed by Waegell and Aravind (J. Phys. A: Math. Theor. 45 (2012)
405301), seems to be intricately linked with automorphisms of the hexagon.
Finally, the entanglement properties exhibited by edges of both pentagrams and
these particular Waegell-Aravind configurations are addressed.
