Yet another very niche post. Would you like to do this?
This image is taken from https://mathcraft.wonderhowto.com/how-to/make-platonic-solids-out-playing-cards-0130512/ – however the templates document that this page refers to is no longer available, and there’s no information on the underlying maths either.
I’m trying to figure out how to build more complex stuff of this type, so I figured it was worth sitting down and working it out from scratch. See below for both the maths, and the cut angles for all 5 platonic solids.