Knot theory: Genus of a surface Use Euler characteristic to determine the genus of the surface in Figure 4.24 in picture below.
I am stuck with this question 4.10 from Colin Adams, the Knot Book.

This question came up today in my class.  The isotopy above is probably the easiest way to see that $g = 2$ but one can also count as wiiza did - (we did this together!)  However, in the spirit of the section - there's a shorter way (shown to me by a student) by just subdividing so that the faces have disks as boundaries.  It's a bit of a head twister, but here's a photo: 
