It is done. This pattern by Lee Hye-oon is found in her book Lovely Tatting Doilies for Spring and Summer on page 105 but you can also find it on Lovely Tatting here.
This was tatted in Lizbeth Size 40 Col.185 Artic Waters. I had thought I would run out of thread but it was sufficient. While blocking, I realised a mistake. I have corrected it but it was after this photo was taken. See if you can spot it.
Now I can focus on Alice, the doily I am tatting now.