Thanks very much for such a detailed response Brian. Thanks also for the paper model tutorial which is very useful.
I’m having difficulties with your explanation though.
What is the best way to split a curve with a line? I tried projecting a line onto the surfaces and using the resulting lines to split the curves but sometimes it works and sometimes not.
I didn’t understand how to create patch surfaces either.
Also, in the last model, that edge piece is solid. It’s perhaps not easy to see in the diagram I posted but the final diagram is not a solid but a surface. The idea is that the object would be cut into corner pieces and then printed on paper. The paper would be folded along the edges that were created in the ‘conical extrude’ step. These pictures hopefully show what I mean.
In case you are interested, this is the source of his project: