Found a bit of a method. Created a polyhedron in mesh modeller. Applied extrusion with "link polygons" unchecked. Hid those, deleted the original polyhedron, brought them back. Then a manual step; linking the centers a la the "spreaders" of a real dome. Filled all, emptied the triangles, applied "add thickness" to the remainder. Turned on Subdidivision Surfaces and selected each "spreader" with the marquee tool to crease the edges there. About twenty minutes all told. I'm noticing now that I'm rendering that the squared-off edges are a bit obvious. A little more cleverness with the extrusion tool and you could get a better cross-section going, I bet.