I am willing to know the visual concept or communication behind such logo designs like IDEO's forming or surrounded by a flat square shape and contains only 4 letters or symbols. See the images as attached.
I don't think there's any particular 'concept' at work. It's just a nice, geometric way to organize 4 elements.
Squares are sturdy and solid, and as a logo, fairly versatile (they aren't particularly horizontal nor vertical)
(Note that the second image isn't actually a logo, but a piece of artwork: http://www.marketingprofs.com/opinions/2007/21492/art-or-logo-how-a-familiar-four-letter-brand-affects-perception)