Geometric Structure of Chemistry-Relevant Graphs: zigzags and central circuits
CORRECTIONS, ADDITIONS AND UPDATES:
In particular, any {\index{\em bifaced map}} (i.e., $(\{a,b\},k)$-$\mathbb{F}^2$)) have, by Euler formula, $$ p_a=\frac{b(k-2)-2k}{2k-a(k-2)} + \chi(\mathbb{F}^2)2k.$$
In particular, any {\index{\em bifaced map}} (i.e., $(\{a,b\},k)$-$\mathbb{F}^2$) have, by Euler formula, $$ p_a=\frac{p_b(b(k-2)-2k)+ \chi(\mathbb{F}^2)2k}{2k-a(k-2)}.$$
Chapter 5, Page 100: in Fig. 5.1 change all 3 symmetries C_{2\nu} on D_{2d}