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Bot Shape
Personally I am all for the sphere idea, but good luck getting that to work in a KotH.
A circular base has lots of advantages you dont have to worry about corners on the playing field, you dont have to worry about protecting your corners, and the strength of a perfect circle is very nice, but there is also the problem that the size limitations are rectangular, so your robot would have a major size disadvantage seeing as you would have to build up instead of out, which is horrible for balance.
Triangle is just odd although if you did something like a triganol pyramid (4 triangular faces) then it could be rather useful if you were flipped or something because with just 4 wheels, two along one edge and two along its opposite skew edge, you would always have driving wheels on the ground. But yet again this is faced with the size problem.
Square, or rectangular, is seemingly the best of what you listed simply because of the way size regulations are set up. With the box your robot has to fit in having a rectangular bottom, the best way to optomize space and sit as low as possible is to spread out as far as possible in that box.
Personally though I think a design for a pentagon shaped bot would be cool. However, you can't completely determine the shape of your bot until the game is released, you do need to build your robot around the game and not around what everybody else does. I know our bot will most likely be rectangular again this year, but we will once again be more concerned with our drive train than we will with shape. I know last year we were one of the few robots that had multiple gears and could shift them on the playing field.
Good luck with whatever you design though.
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