A is for A-frame.
Thanks to the keen eyed Caperberry and the trigger finger of BrickOwl, this part was brought to my attention before release of any sets featuring it. I had to obtain a few for my angling pleasure.
It's a very odd part. It's like a fixed 1x4-1x4 plate hinge. With struts in the middle. And no hinge knob. And it's at exactly 45°. While 45° makes a lot of sense, I sincerely hope that a similar 60° plate is in TLG's future.
My first thought was to connect 8 of them together. Sounds legit, right? The result is a very fine crosshair, spider web, or basis for an octagonal SHIP component.
The inherent problem with 45° is that the hypoteneuse will never be an even number. Thankfully we don't have to go TOO far before we get within a relatively acceptable tolerance. With 5 stud legs you can force a 7 stud hypoteneuse. To wit, 5² + 5² = 25 + 25 = 50. √50 = 7.071. Pretty close tolerance at 1%. Theoretically you could do legs of 10 studs. But while the tolerance is still 1%, that's about 1/7 of a stud in distance or near 1mm. Another sweet spot (known to roof framers for creating hips) is that 12² + 12² = 144 + 144 = 288. √288 = 16.97. This is even closer at 0.1% off, or about 1/34 of a stud. That's 1/4 of 1mm; hardly even noticeable! Other variations are possible though the size of your built up brace is going to get very large.
You might also stagger them to get a nice little spacing effect. Mathematically speaking there should be space enough for a sideways tile. Practically speaking, there is.
Then I wondered what could result if they were connected in 3-D. I get a little lost with 3-D angles myself. Advanced Trig was not my best subject. Mostly I go off of trial and error with a pinch of gut feeling. Nonetheless, I was able to make a nice little stand for half of Bespin.
These parts may not be earth shattering in the job they can do, but they certainly offer a lot of stability not seen in parts like plate hinges. I can see this being the next big thing in 2014. Not always a featured part, but a highly utilized structural part. If you'd like to play around with a few, I've got 16 shiny new ones available for sale in my store. Make an offer on multiples.