vec p q = zipWith (-) q p
add p v = zipWith (+) p v
mul u v = map (u*) v
dot v w = sum $ zipWith (*) v w
sqd v   = dot v v
len v   = sqrt $ sqd v
dir v   = [x/l|let l=len v,l>0,x<-v]
rot [u,v,w] 
    [x,y,z] = 
    [v*z-w*y, w*x-u*z, u*y-v*x]
tra     = [[[-1,0,0],[0,0,0],[sqrt 0.75,0.5,0]],
           [[-1,0,0],[0,0,0],[-sqrt 0.75,0.5,0]],
           [[-sqrt 0.75,0.5,0],[0,0,0],[-1,0,0]]]
tri t   = [[b,c,add d (mul s e)]| [a,b,c]<-t,
	   let d=add c (mul 0.5 (dir (vec b c))),
	   let e=dir (rot (vec a b) (vec b c)),
	   s<-mul (sqrt 0.75) [-1,1]]
main = putStrLn $ unlines $ map show $ concat $ concat $ take 12 $ iterate tri tra