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.)
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.