Steiner System
The Fano plane, as a block design, is a Steiner triple system. As such, it can be given the structure of a quasigroup. This quasigroup coincides with the multiplicative structure defined by the unit octonions e1, e2, ..., e7 (omitting 1) if the signs of the octonion products are ignored (Baez 2002).
Read more about this topic: Fano Plane
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