jwaytogo: I think you could call it a double wing formation if it is from a hoshi, but it is not as elegant or significant as a double wing from a shimari. The shimari version is harder to invade or reduce. If it is from a hoshi, it sounds just like the ideal situation to invade the 3-3 point. Just my 2 cents worth.
George Caplan I agree with the above comment, with the exception of the word "elegant". Elegant in go usually implies efficiency or simplicity - obviously none of these are precise terms. My argument would be that, if anything, the double wing from hoshi is more elegant - in that it is faster and more efficient, making a moyo using three stones instead of 4. Based on a shimari, the double wing is more significant - in the sense that it has more territorial value and is harder to reduce.
Andy Pierce: I prefer it to be mandatory for a "double wing" to be based on a shimari. If the body of the bird is not in place, the wings aren't much of a threat.
Chris Hayashida: Double-wing formation is used for extensions on both sides of a corner. I have seen it used in books for shimari, 3-3 points, and 4-4 points. The term "double-wing formation" does not imply that value strategically. It describes the extensions from the corner. Each of these can be invaded and reduced.
Hiker: In my high kyu games, I often try to form a Double Wing formation. I am amazed how often my opponent will let me. I am often told that such things would never be allowed to happen in higher skilled games. How often does it happen? I'd love to hear other's opinions of advantages and disadvantages of attempting this formation.
Bob McGuigan: Double Wing formations happen often even in professional games. While these may be good formations, like most things they depend on what is happening elsewhere on the board. With good play, a player who gets a double wing formation must have given the opponent something good elsewhere. Also, there are standard invasion and reduction techniques for these formations. This is a big topic. Here are some pages to get you started:
Reducing an enclosure framework by capping
Reducing an enclosure framework by a shoulder hit
If you can find a copy, Takemiya's book Enclosure Josekis has a lot more information. Another good book on this topic is Iwamoto's Keshi and Uchikomi - Reduction and Invasion in Go.