I’m trying to use this closed curve in the center of the ring to wirecut the solid triangles on the top, but I can’t get it to work. The solid triangles are closed polysurfaces without any naked edges or bad surfaces that I can find. Any ideas?
I would extract that surface, make curves from the edges and use the long edge curves as rails to sweep the two end curves. Join the new surface into the triangle in place of the old one and see if that gives you a closed polysurface. If not, be prepared to match the adjacent surface edges to the new ones.
When closed, try the wirecut again. Let us know how you get on.