Pattern calls for Japanese size 7 knitting needles (4.2mm).
The pattern stitch is called 変わりゴム編み (brioche).
Due to overwhelming demand for further assistance for the construction of the hat, Nihon Vogue has created [a page to assist knitters in putting the hat together][1].
[1]: http://www.tezukuritown.com/book06/6425/01.html