Finding the core of a 4 player game

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How do you find the core of this game?

$V({0}) = V({1}) = \dots = V({4}) = 0 , V({1,2,3}) = V({1,2,4}) = 6, V({1,3,4}) = 5,V({2,3,4}) = 3, V({N}) = 11$

This is supposed to be the core: $C(v)=conv( { (6,0,5,0), (0,6,5,0), (8,0,3,0), (8,0,0,3), (8,3,0,0), (6,0,0,5), (0,6,0,5), (5,6,0,0), (1,0,5,5) (0,1,5,5) } )$ Where $conv()$ denotes the convex hull of the set of allocations.

I don't see why for example: $(0,0,5,6)$ is not in there and why $(1,0,5,5) (0,1,5,5)$ are in there