g = pi/3, p = pi/2, v = 2*pi/3
NOTE that d(x,-a)= pi - d(x,a).
1 i j k a a^2 b b^2 c c^2 d d^2
1 0 p p p g v g v g v g v
i p 0 p p v v v v g g g g
j p p 0 p v v g g v v g g
k p p p 0 v v g g g g v v
a g v v v 0 g p v p v p v
a^2 v v v v g 0 v p v p v p
b g v g g p v 0 g p v p v
b^2 v v g g v p g 0 v p v p
c g g v g p v p v 0 g p v
c^2 v g v g v p v p g 0 v p
d g g g v p v p v p v 0 g
d^2 v g g v v p v p v p g 0
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