The book's cover, the cover of the book or the book cover

All three are fine. "Of" does not just denote belonging but also:

A relationship or connection:

The secret of this game is that you can’t ever win.
The highlight of the show is at the end.
The first page of the book describes the author’s profile.
Don’t touch it. That’s the bag of my friend’s sister.
I always dreamed of being rich and famous.

Reference:

I got married in the summer of 2000.
This is a picture of my family.
I got a discount of 10 percent on the purchase.

An amount or number:

I drank three cups of milk.
A large number of people gathered to protest.
I had only four hours of sleep during the last two days.
He got a perfect score of 5 on his writing assignment.

Wow Cen you sure get into this stuff deeply

I was gonna thank you for the Prof til I realized it was in Latin or sumpthin'.

If I seem repetitiouos it's old age and decaying brain

Still for some reason I remain curious about everyone because I just don't consider it possible to adequately address someone's posting without knowing more about him

If you like to chat I am [email protected] and yes I'm considered idiotic for such a revelation