These parameters include table, crown height, pavilion depth, girdle, culet, and depth, according to Tolkowsky's calculations for maximum brilliance and a recent change in table diameter to 59%
(some complicated reading and further details). For my particular solitaire, it has nearly perfect proportions (within 0.10%) as Tolkowsky with the modified 59% table diameter.
It literally directs every beam of light exits the top of the stone and sparkles from every angle, even in the shade.
The most ideal diamonds from wholesalers will cost only a bit less than a Tiffany diamond because it is
that difficult to create a diamond with these proportions.
It is true that you can buy a diamond with the same 4C's as a Tiffany for thousands less. But mathematically and subjectively speaking,
it will not possess the fire and brilliance of a Tiffany/ideal diamond if it does not have the ideal proportions, and you can easily see this when comparing. An ideal diamond is expensive no matter where you go, but diamond shoppers are often only concerned with the 4C's and not so much the cut proportions which makes all the difference in the world. Additionally, round brilliants offer the most brilliance and fire because of these proportions -- however, that isn't to say that non-RB cuts are not pretty, but they are, quite objectively, not as sparkly.
A Good start on technical information, some misinformation, but we aren't teaching a class & its probably more than most diamond buyers know.
To be considered a GIA ideal cut diamond, its specs need to fall into a certain range or it can't be classified an GIA "ideal" diamond. So an ideal diamond is an ideal diamond whether its from a broker or Tiffany. They are the same thing. All other issues identical, One is not going to have more fire than another. If you want to buy from Tiffany, great! But to say theirs are the best & only they get them is a marketing lie. Many of us started our searches at Tiffany for the basic education & then spent months doing research. Harry Winston & Graff carry an even better line, bigger stones & many fancy rare colors.
I am contantly amazed that what is one of the most expensive purchases many people make & they do little to no homework on buying diamonds. The 4 c's is just getting started.
Many people have the connections to get these GIA Ideal diamonds from brokers. We buy all my stones from one, he is in the highest ranking for brokers in his profession & gets the required stones shipped to him, I fly there & can spend as much time with each stone as I want, taking them outside, comparing them to each other etc.
I've done the ego thing, I'm over 40. Or if I did need the boost, I'd buy from Graff, that's a very exclusive diamond store! But I don't need to feel superior or get any satisfaction about having to buy it at the blue box store. When I've been in tiffany's looking, they've cleaned my ring too.
I want a stone that when I tire of it, (its 4.1 ct so that's not happening soon) The broker will buy it back or it'll go to Sothebys or Chrisites. Broker's already called DH & offered him double what he paid 8 years ago, said he has a buyer for it. I can't do better quality wise & I don't want a bigger stone, so I'll keep this one. I am thinking about adding 2 side stones of 1.5 to 2 ct on each side though.
While a Tiffany diamond may be a better cut than other "ideal" cuts, the average person on the street is probably not going to appreciate the difference. 
I love Tiffany's. While there are perfect reasons why someone else's diamonds are just as good, their presentation is always spectacular. When my hubby proposed, it was a Tiffany-style setting, round-cut and 1.3 carat, E, SVV1. It was the best he could afford, and that said, it meant more to me than anything else.
