It has taken me an age and been very tricky mostly because of trying to work out the 3D composition of the upper part of the chair - and apologies for the lack of pictures thus far.
So here is the base... construction was, like the writing table legs, done with an MDF curved template cut to shape, then a bearing-guided flush trim bit, then a bearing guided thumb moulding bit to make the curves. Once the 4 legs were roughly finished, they were joined together with dominos, then the 4 quadrants added for strength. Finally I added a 4cm piece of ebony to the bottom of each leg, again domino'd in place. It seems quite strong
For the top, I joined 2 of 10 inch wide, 2 inch thick pieces of olive ash, then cut the circular base from that. I used the new proxxon long-neck grinder with mini Arbortech blade to cut out the seat, then used a Rotex sander to smooth it. The mini grinder is absolutely great and very easy to control although dust extraction is obviously very limited.
The top frame was done using the table saw to cut compound angles on paired pieces of 4x2 olive ash starting from the top middle. Each piece was joined to its neighbour using a single 10mm domino. This was complicated as I was going to remove a lot of waste once it was all glued up so that it all flowed together and I obviously did not want to expose a domino accidentally so I had to try and place them in the centre of where I thought the final shape of each piece would be.
Once the basic form was complete, I used the long-neck grinder again first with the mini Arbortech and then with the fan sanding attachment which were superb.
The 'supporting struts' of the top were easier and no problem joining them to the base. Then the only difficulty was joining the top frame to the tops of the legs - I ended up using an 8mm dowelling set - but then once the dowel was in place roughly, I drew round the top of the leg on the bottom of the frame and cut a 1/4" recess into which the legs fitted exactly.
I was delighted with the swivel - only GBP10 from that marine store