Nonexistence conjecture for face-transitive Klein bottles

A face-transitive Klein bottle is a simplicial Klein bottle whose face-transitive symmetry property is understood in the sense of the paper's census. Face-transitive Klein bottle conjecture. There is no face-transitive Klein bottle. The conjecture arises from the census: no non-orientable face-transitive surface in the computed list has Euler characteristic $0$, the Euler characteristic of the Klein bottle, but the general nonexistence claim remains open.