I'm looking to make Triangular & Hexagonal shelves, but I'm getting confused by some of the maths involved for the bevels. To make a hexagon I need a 120 degree angle, but I need 2 pieces to make that angle, so I do: 120/2 = 60 degrees each.
So I would think that I can set my bevel gauge to 60 degrees on my table saw (Hypothetically, I'm aware that my bevel doesn't go that far and that I can use a jig to hold the workpeice vertically to do the complement of 30 degrees, effectively making it 60 degrees)
I'm having similar issues for the equilateral triangle shelves. I've seen people cut their straight stock at a 30 degree bevel and wind up with angles that don't look right, such as:
Here, you see that the shelf is not assembled at the edges, and is instead on the face. This doesn't look right to me, and seems to imply that the person didn't know how to cut the angles properly. I've seen proper bevels cut and they look really nice, even at non 90 degree bevels, such as this one from Foureyes:
How can I resolve these issues? What bevel should I cut my straight stock on, so that I can make these shapes?
EDIT 0: In general, if I want to cut a 30 degree angle in Cartesian space, do I set my bevel gauge to 30 degrees?
EDIT 1: Stranger yet, I've seen the hexagons be cut at a 30 degree bevel by this video (https://youtu.be/_sQzIbgQjig?t=38), and my intuition tels me that a transformation function is used to convert between Cartesian space and table saw bevel space. He needed a 60 degree angle in Cartesian space so he took the compliment of 60 degrees and obtained an angle of 30 degrees, and this is what he set his table saw to. Is this thinking correct?