Thanks all for the kind words.
It's coopered construction. The shape is an isometric ellipse - see the attachment. If you do a search for coopering on these forums you will find a coopering spreadsheet that will give you the widths, thicknesses and angles of the staves.
First I made the inside (blackwood) box, then the silver ash surround, which I cut to shape later. Before gluing the blackwood staves together, the inside was sanded (800), given a coat of shellac and resanded. They were then given a coat of wax on the inside faces to prevent glue (Titebond) sticking.
The sizes have to be measured and cut very precisely. The two pieces have to fit together exactly. You could add a slight allowance on the outer box, but if it's too much, you'll have unsightly glue filling the gaps. I used the exact theoretical size, on the basis that if the outer sleeve was too small I could take a shaving off each inner stave. Fortunately, this wasn't necessary.
All exposed parts were smoothed by planing, scraping and sanding, but the parts of the staves that were glued were left flat.
All parts that weren't going to be glued together were sanded, shellacked and waxed as above. For gluing the inner and outer parts together, I used L139P Epoxy from
Adhesive Enginering, tinted to match the silver ash. This was applied to the mating surfaces, and the inner box slid into the surround. The epoxy acts as a lubricant at this stage. To avoid a mess, sit the box on a sheet of plastic wrap while doing this. There will be a lot of squeeze-out, but hopefully the surfaces where you don't want glue will have been waxed (just any cheap floor wax will do), and after about 5 hours the glue will have reached a hard rubbery consistency that is easy to remove.
Once the glue has gone off you can remove the wax with a toothbrush, paper towel and white spirits - this will not soften the shellac. Make sure you remove all the wax.
The final finish is Kunos oil, cut 50% with Bio-thinners. I apply a flood coat, wiping off any excess after 15 minutes. After 24 hours, apply a thinner coat, well rubbed in. The next day, I apply a coat with 0000 steel wool, removing any excess and rubbing the remainder in. After that, I rub in successive coats with a barely oiled cloth, and buff after about 10 minutes, until it's reached the desired sheen.
Hope this helps.
Elliptical box 
pretty please
