Pergola design – not enough posts?

Hello all,
I am building a 12′ x 14′ pergola, using 4 – 6 x 6 posts (which will be cemented into the ground). Do you think 4 posts are enough? I am going to use 2 x 10 rafters on either side of the 6 x 6, and 2 x 8’s crossing the 2 x 10’s, and finally 2 x 2’s crossing the 2 x 8’s. The only weight this will hold will be the lumber and possibly a vine of some kind.
I was thinking of going ahead with 4 posts only, but I didn’t know if I should re-inforce the pergola by adding 6 x 6 corner brackets attaching from the post in between the 2 x 10’s. The 2 x 10’s are going to span on the 12′ side (due to where the sun is, I will need the 2 x 8’s going to other way to block as much sun as possible).
Last question, I am going to sandwhich 2 – 2 x 10’s on either side of the 6 x 6’s. I will have 4 of these 2 x 10’s then running east – west. The 2 x 8’s I am going to put 16″ on centre and run these opposite the 2 x 10’s, following by 2 x 2’s running opposite the 2 x 8’s. Should I run 2 x 10’s all the way around the posts (i.e. use 8 – 2 x 10’s w/ 4 running east-west, and 4 running north-south, instead of 4 – 2 x 10’s running east-west).
Any help is greatly appreciated!