@The-Blade-Dancer 👏 That's a really good way! 🙂 I like it!

 
M3W4D16-y-question-screenshot.png
 
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.

 
M3W4D16-y-buildling-block-pyramid.png
 

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 \(30 + 30 = \boxed{60 \text{ faces}}.\)

Also I'm pretty sure all those lines on the shape represent shadows. From the pic here, it seems that the light is coming from the upper right. In Prof. Loh's pic, it looks the bottom left, probably because he switched all the darkest and the lightest parts here.