Tom, there several ways to accomplish this type of effect. The simplest would be to cut "simple" (not compound) mitered segments from over-sized material. The trick is to cut all the angle on just one side of the segment. For example, if a normal segmented ring were constructed with 8 segments, each side of the segments would be cut at 22.5-degrees. To achieve this twisted effect, you simply leave one side at 90-degrees and cut the other sides at 45-degrees. When the segments are squeezed into a round ring, they will slightly rotate and create this type of effect. Hope that all makes sense.