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Re:Clifford Algebra: A visual introduction (2014) by jnwrd on Friday June 19, 2015 @06:29PM (#9748062)
There is actually a 7-dimensional "cross-product" (-esque operation): https://en.wikipedia.org/?title=Seven-dimensional_cross_prod...

The relationship between Quaternions and the 3-dimensional cross-product corresponds to the relationship between the octonions and this 7-dimensional cross-product. Normed Division Algebras are a fascinating and worthwhile subject to look into.

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