A Class of Three-Qubit Contextual Configurations Located in Fano Pentads

Given the symplectic polar space of type $W(5,2)$, let us call a set five Fano planes sharing pairwise single point pentad. Once 63 points $W(5,2)$ are appropriately labeled by non-trivial three-qubit observables, any such pentad gives rise to quantum contextual known as Mermin pentagram. Here, it is shown that also hosts another, closely related set, which features 25 observables and 30 three-element contexts. Out ten each them on six contexts, while remaining 15 belongs two contexts only. Making use recent classification pentagrams (Saniga et al., Symmetry 12 (2020) 534), was found 12,096 sets comprise 47 distinct types, falling into eight families according number ($3, 5, 7, \ldots, 17$) negative