Clark’s article shows a good technique to change-up the longer L:W emerald shapes. His first design seems similar to a 1979 design titled “Fantasy Cushion” that I’ve used many times (and seems poorly named for today’s cutting world). There are several variations on the theme at this URL, however without instructions: Facet Diagrams for Cutting Gemstones - FacetDiagrams.org
The second design in Clark’s article is novel to him as far as I know – and looks well worth the trouble of cutting it. I’ll give it a try myself sometime.
But I was surprised that the article here on IGS doesn’t have any images of either design in a finished stone. Here’s a recent stone I cut in my variation of the Sparkling Emerald or “Fantasy Cushion” design; not exactly the same as Clark’s design, but close enough for you to get the idea.
Tourmaline (Nigeria). 6.15ct, 7.63x14.61x7.22mm. Heated. Custom Emerald. (Tour1590)