Delivering now! I'll walk you guys through the creation of all the bindpoint arrangements - 6, 4, and 2, followed by the top secret 5 and 8 not yet discovered in the books!
Animation - So, we'll do 6 first because it's the easiest. Simply start with your initial 3 bindpoints equidistant from each other, so the triangle they create will be equilateral. The reason that this creates 6 bindpoints instead of 9 is because 3 of them overlap.
Animation - Next up, 4. to make this one, imagine a square inscribed in your circle, and then take three of the corners (doesn't matter which) and make them bindpoints. The big triangle you draw will have one of its corners resting right on the circle!
Animation - Now, 2! This one is the hardest to wrap your head around. You have to make 2 of your bindpoints overlap, and put the other one on the exact opposite side of the circle, which will make a straight line instead of a triangle! Well, you can think of it as a triangle with 2 sides that are twice the diameter of your circle and one side with no length at all. Now you might be thinking, "Why does the last point have to be exactly opposite of the other two? Why can't I put it wherever I want since I'd still get a straight line?" The answer to that is a little in-depth, so I've put it in a spoiler tag. Read it at your own peril!
Animation - Okay, to make a 8-pointer couldn't be easier. Just start our with your initial bindpoints equidistant, like you did with the 6-pointer. This makes the triangle equilateral. Now, move two of the bindpoints along the circle, one clockwise and one anticlockwise, making the triangle an isosceles. Basically you've stretched the triangle upwards. The strange thing is that Rithmatists don't use this shape, even though you can make it into a nice regular octagon. Off the top of my head, the Eskridge Defense could be modified to used 4 defensive walls instead of 3, possibly offering greater maneuverability and offering stronger defense.
Animation - Last but not least, the 5-pointer. It's very similar to the 8-pointer, except you start with a 4-pointer instead of a 6-pointer. Jeez, pointer doesn't even sound like a word anymore. Because of the lopsided nature of this one, I can't really imagine it being useful in the Melee.
That's a wrap, folks! I know all of this was old news thanks to advanced Rithmatists like kalynaanne (except for the last line in the obtuse triangle section), but in my next post I'll be going a little farther into the unknown. Why a nonagon? How does the circle "know" to be weaker if it's bindpoints are wrong? I mean, surely there isn't a shadowblaze doing the math in its head every time a rithmatist draws a bindpoint. Tune in next time to find out!