According to those calculators, no 55 or 75 gallon tank with 1/4" glass should be on the market--but they are. So it would seem that they are oversimplifying things and don't really offer an answer to my question.
I guess what I should have asked was:
If the front and back panes on a 55 are fine for that application, is there any good reason why they wouldn't be OK to be used as the sides, front and back of a 4'x4' tank?
Most 55s are tempered, and that makes a difference. A 75 gallon tank with 6mm glass will most certainly be tempered, or the water would be outside the tank. (depending on dimensions.) One cannot look at a manufactured tank, that are often horribly under built (look at the cube tanks that use 6mm glass, and are popping seams with some regularity,) and expect to learn anything about building tanks.
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Tank building is a very highly specialized craft that requires some engineering skills, knowledge of material strength (in a given and specific context) and water pressure; knowledge of what "strength" is important, and what "strength" is irrelevant. For instance, the tensile strength of silicone is irrelevant: because it is not the weakest link in the chain.
After building tanks for better than 20 years, I (and many other professionals) have come to the conclusion that tank building is not something that can be taught via the web, whether it be videos on youtube (the worst place to get information put out by self-promoting diyers that are lucky they don't need liability insurance) or by reading posts in a forum. The best that can be done is hopefully keep people out of very serious trouble, but the outcome of the build still has so many variables attached to it, it is impossible to predict it.
In most all cases, a person asking questions concerning glass thickness should not be building a tank, and it would be far better and safer to buy a tank of similar dimensions. Depending on where the tank is purchased, it could very well be under built, (production tanks always are,) but at least there is a warranty (if you do what they tell you to) to cover the catastrophic damage if the tank decides to self-destruct.
For the first tank mentioned in this thread:
15mm sides and ~ 19mm bottom for rimless, internal euro-braced bottom can be 15mm. A professional could build this with 12mm, but an amateur should not even consider it. The extra 3mm just might save the day, if other constructions methods fall short, and it is highly likely they will.
10mm is the thinnest glass that should be used, and that would need a full rim; 12mm running next with a euro-brace. (top and bottom.)
This is not a contest of cost, weight, or availability—it is about keeping the water inside the tank. In terms of cost it will most often cost less to buy a tank, or have one built for you.