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How to use the intersection triangle of the Steiner System $S(5,6,12)$ to show the completement of any of its block is also a block?

My argument: Since the parameter $m_{60}$ in the intersection triangle is 1, so each block $B$ has a unique block $B'$ which is disjoint to the former, thus $B' \subseteq X\diagdown B$. Moreover, since $|X\diagdown B|=12-6=6=|B'|$, so $X\diagdown B=B'$ which implies $X\diagdown B$ is a block. Is my argument valid based on my interpretation of $m_{60}$?

For the convention of the subscripts please Google the book “Topics on Steiner Systems” By Charles C. Lindner, A. Rosa, on page 49

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    I don't have any copy of this book. Can you please give me the meaning of the notations $m_{60}$ and definition of intersection triangle ..So that I can understand your argument.2012-05-24

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