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Summary
DescriptionFanoPlane with GeometricAlgebra.svg
English: This is an illustration of the Fano plane in 3 forms (e_n, IJKL, and Hodge star Geometric Algebra) with multiplication matrices in both e_n and IJKL format. A complete list of all 480 octonions and their Fano plane and multiplication tables (in two parts) are here and here. (.pdf 80MB each). A description of the Mathematica algorithm with code is here.
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This is an illustration of the Fano plane in 3 forms (e_n, IJKL, and Hodge star Geometric Algebra) with multiplication matrices in both e_n and IJKL format