@The-Blade-Dancer That's a really good way! I like it!
Another slight variation on this method is to say that the 3-D figure is composed of the same repeated building-block, the pyramid with five triangular slant faces.
On our side of the shape, there is a big 5-pointed-star looking at us, and it's composed of \(6\) of these building-block pyramids, so the 5-pointed-star contains \(30\) faces. The side facing opposite from us contains the same 5-pointed-star, simply rotated, so it provides another \(30\) faces.
The total is \(30 + 30 = \boxed{60 \text{ faces}}.\)
