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Design theory is the subfield of combinatorics concerning the existence and construction of highly symmetric arrangements. Finite projective planes, latin squares, and Steiner triple systems are examples of designs.

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Octonions and the Fano plane.

Does the Fano plane mnemonic for octonion multiplication have any deeper meaning? http://upload.wikimedia.org/wikipedia/commons/2/2d/FanoPlane.svg The symmetry group of the Fano plane is PSL(2,7), t …