# Intersection triangle of Steiner System

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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Since there are 12 points, two disjoint blocks of six points each must clearly be the complement of each other. Assuming the $m_{60}$ means what you think it does (I cannot see that page in googlebooks) then what you wrote is correct. –  Mariano Suárez-Alvarez May 24 '12 at 6:50
"No eBook available", so hard to tell. Otherwise obviously agree with Mariano –  Jyrki Lahtonen May 24 '12 at 7:04
Along with a googlebooks link, it would be helpful if you always provided a bibliographic reference to the book —title, authors, edition— and a location in the book, if needed: it may well happened that someone has the book but not access to that page in googlebooks! –  Mariano Suárez-Alvarez May 24 '12 at 7:20
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. –  users31526 May 24 '12 at 7:57