* * * There is 2x 16=32 degrees. Because there are three 4-degree vertices and four 3-degree vertices. That is 3x4+4x3=24 degrees.

That is to say, the remaining vertices * * * have 32-24=8 degrees, and then consider how many vertices there are:

Because the degree of the remaining vertices is less than 3, that is, 0, 1 or 2, that is, the remaining vertices are infinite at most and 4 at least.

Considering that the vertices of odd degrees are even (4), there can be four vertices on them.

That is, there are at least 4+4+3= 1 1 vertices.

I hope I can help you. . . .