Streptohedrons (Part II) - Here are 3 more

I have now turned three more streptohedrons, these based on some of the examples and plans in Woodturning Full Circle.

The first of these is a variation of a Four Branched Streptohedron, which has a kind of art deco shape.  It is turned as a series of right-angled "stairsteps" on each side, as indicated in the photos.  (Cherry, finished with Watco Danish Oil.)

The second streptohedron is a Twisted Pentagon.  Because of the additional side there is an additional axis available, giving the possibility of two variations in the final shape.  Here's what it looks like (Cherry; Watco Danish Oil finish):

The third streptohedron in this group is a Six Branched Streptohedron, with its center of rotation through the valleys.  The turning process here is rather more complex, and it is difficult (at my skill level, at least), to make the cuts precisely enough to get a perfect match-up when the two sections are rotated.  Here are some photos showing the overall approach:

Initially the blank (previously divided lengthwise and re-glued with a paper insert) is turned to the desired diameter; lines are drawn on the circumference to indicate the cutting locations;  and a tapered hole is turned in the end, using a template for size and shape:

Then the first of the shaped sections is turned; again a template is used to get the inside angle correct:

Here is the mostly turned blank.  The left (headstock) end is still fastened in the chuck.  The right end, where the tapered hole is shown in the first photo, is simply supported by the live center.

After the shaping is done, the piece is parted off at the headstock end.  It is then reversed into a jam chuck (a wooden block with a hole turned to hold the piece snugly), and a matching tapered hole turned in the other end.

The piece is then removed from the lathe, and re-split along the glue line into two halves.

The halves are then rotated so as to form the streptohedron and glued together.  The piece is then sanded and finished.  In this case I used several coats of black gesso as the finish - it is both dramatic and disguises minor defects pretty effectively.

The smooth outer rim of the resulting piece is continuous, having neither beginning nor end.  Pretty dramatic, I think.