Thanks, it is a cool looking dish.
You can do these with any number of sides. You might want more sides on a larger turning. I had a square block of maple. I found center and drew the largest circle I could. You can start with a round block as well but if it has not been turned round and already has a center, you need to find center and draw a circle to get an exact diameter.
Draw one radial line from the center to the circle . This is your 0 degree line for your protractor. I used a 360 degree protractor and didn't have to move it.
Just mark around the protractor in even units depending in how many sides you want on the dish or bowl. For this I used 72 degree increments.
Mark these lines out to the drawn circle and then draw between points to get the sides. I used the bandsaw to cut these sides, hit the edges on the disk sander before mounting between centers on the lathe.
While between centers, I turned a tenon on the bottom of the dish for my chuck to grab....mount in chuck and start turning. Sharp bowl gouge and light cuts are key.
I turned the outside shape first and then followed the profile while turning the inside. I used a block with sandpaper of hand sand the flat edges to clean ip a tiny bit of chipping on the trailing edge and to clean up the disc sander marks.
After that, it is just standard hollowing once you get past the wings.
Use a power sander with wavy discs to sand the wings with the lathe off. It takes some care to meet the edges from getting too thin and uneven.
When sanded, I turned it around, jamb chucked it( still had my center on the bottom) and turned the tenon into the foot, leaving just the center nub.
Off the lathe, I used a dremel to clip off the nub and power sanded the bottom center...Done!
As for turning a lot of air, these wings didn't extend too much in depth or diameter. The more points you have, the less air you have, this one was not bad at all. Also, turn a little faster since you have air spaces.
Good luck! I would like to see some of your winged turnings!