These tables from British furniture designer David Fletcher are made on commission for wealthy clients who, apparently, mostly want to install them in their yachts. Each table reportedly cost tens of thousands of pounds. Both manually- and servomechanically-actuated versions (upper and lower videos, respectively) have been made. Without meaning to take anything away from the craftsmanship that is evident in Mr. Fletcher’s work, I’d be surprised if this design couldn’t be reverse-engineered and produced, perhaps in a smaller version using a CNC mill, at a non jet-setter price.
Some observations: The table top pieces are only truly circular in their larger arrangement. In the “contracted” table, the 6 wedges in fact form a kind of rounded-off hexagon, and the outer table edge is made circular by the rotating rim, which has a complementary inner profile. Besides the wedges, there are two other types of pieces that make up the table top–6 “darts” having two parallel sides that rise to fill the spaces between the wedges, and the “star” (a dodecagram, in fact) that rises up in the middle. The table is locked in either configuration by one or more threaded detents which are quite clearly shown in the upper video.
So the geometry of the dissection is straightforward enough. The real challenge would be to remake the mechanics on a budget.