The central-circuit characterization of maximal irreducible hedrites

Let $i$ be the number of faces of an irreducible $i$-hedrite, and let a central circuit be a central circuit of the hedrite. An irreducible $i$-hedrite is maximal irreducible when it cannot be extended while remaining irreducible. Central-circuit characterization. An irreducible $i$-hedrite is maximal irreducible if and only if it has $i-2$ central circuits.

The surrounding discussion gives examples of irreducible $i$-hedrites with $i-2$ central circuits for the relevant values of $i$, and notes that these examples are pure. The parser supplies no evidence resolving the stated characterization, so its status remains open.