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To construct a building, first you need a Coxeter Group......

http://en.wikipedia.org/wiki/Bruhat-Tits_building

Let Gravity equal to the square root of -1! Muahhahah!

he should design spaceships!

But then it wouldn't be easy anymore, it would be complex

First rule of Engineering - Make Reasonable Assumptions

Never! I want my spherical cow!

I think the mathematician would try to build it for all gravitational fields, or can we say without loss of generality g=0?