I was able to locate the articles that describe some pretty complex ways of laying up wood for the carved Shell Niche (also referred to as “Cockleshell” carving). There are 3 that I could find and all are from Fine Woodworking.
Sept 78, #12 – “Cockleshell – giant carving gives corner cupboard class” by Franklin H. Gottshall
Feb. 92, #92 – “Router-Assisted Cockleshell Carving – A swinging jig shapes the interior and defines the flutes” by Howard Wing
January/February 92 (not sure what number – probably #92 also) – “Gluing up a shell with tapered segments” by Philip C. Lowe and Justin P. Smith
The process I used was much simpler than any of these techniques. I’m not an engineer, and the people who wrote the articles above are obviously much better at figuring out these techniques. My process is get it there the quickest & simplest (although many times it does not end up that way).