I hadn't ever seen these forms before, and was fascinated. I turned the form described in the article (shown below), and then acquired David Springett's amazing book, Woodturning Full Circle, which (among many things!) includes sections on how to turn a variety of streptohedrons of different configurations.
As defined by Springhett, who appears to have invented the term, a streptohedron is a "twisted polygon," that is, a polygon which has "rotational symmetry": when split along an axis, rotated, and rejoined, it becomes a new shape with "compound-curved faces that seem to flow smoothly into each other." (Rollings) The beginning polygon can have any number of sides. To turn one you prepare a blank, split it down the middle, and then glue it back together with paper in the joint. You then turn the specific shape you want, re-split the piece along the glue joint (and clean up the faces), rotate ("twist") one section in relation to the other, and then glue them back together. If (!!) the turning has been done precisely, the edges will line up and the streptohedron emerges. A little - or a lot - of careful sanding also can help.
This is the first streptohedron I turned, based on the AW article. It has four "sides." The wood is Claro walnut.
Here is the glued-up blank, turned to shape between centers on the lathe:
Then the turning is re-split along the glue line:
The two pieces are then turned 90 degrees and re-glued to create the new, complex form:
Once the glue is dry, the piece is completed - the extended ends removed, the piece sanded, and finish applied. Here is the result (finished with Watco Danish Oil):