User blog comment:Hyp cos/SCG(n) and some related/@comment-1605058-20140915163630/@comment-5529393-20140915171908

Yes, by the 28th step you get to a triangle fused with a polygon. Goucher's sequence goes on an unimaginably long time with fused squares, and then we could do the same triangle fused with polygon sequence, so that is surely better.