This video has some painful PR to watch, but it is probably less painful than reading any description I could write of the project. (There is no audio.)
This 3:32 time lapse is easier to watch than the 1.30 version and includes some activities such as interior work and removal of the drydock wall to float the base out to deepwater.
More videos and photos.
Someplace on the web site I read a description of the slip form construction technique, but now I can't find it :-( The time-lapse videos of the construction of the upper part of the platform shaft does show that slip form construction can vary the shape of the cross section as the forms rise. The videos also shows that several concrete pump trucks were needed to pour a new layer before the previous layer sets up.