I can spot 9 faces.

Found this cool test for divisibility by 7 on Tanya’s website. Read about how to use it here, but basically you follow that diagram a certain way.

Divisibility by 7 :-

and yes the graph is planar.
1. Write down a number n.
2. Start at the small white node at the bottom of the graph.
3. For each digit d in n, follow d black arrows in a succession, and as you move from one digit to the next, follow 1 white arrow.

For example, if n = 325, follow 3 black arrows, then 1 white arrow, then 2 black arrows, then 1 white arrow, and finally 5 black arrows.

If you end up back at the white node, n is divisible by 7.