The weakly neighborly polyhedral maps on the non-orientable 2-manifold with Euler characteristic -2 (Q1091610)

In this paper a classification is given of all weakly neighborly polyhedral maps on the Klein bottle with one handle, compare the general treatment by the authors in Isr. J. Math. 53, 137-157 (1986; Zbl 0592.51016). It is found that there are exactly 8 different maps of that kind, 6 with 9 vertices, 16 triangles and 3 quadrilaterals, 2 with 10 vertices, 15 triangles and 3 pentagons. The proof follows the pattern of the corresponding result for the orientable surface of genus two in which case such a map does not exist, see the authors in J. Comb. Theory, Ser. A 42, 87-103 (1986; Zbl 0585.57004).