Combinatorics and Graph Theory


The Comprehensive Split Octonions and their Fano Planes

Authors: J Gregory Moxness

For each of the 480 unique octonion Fano plane mnemonic multiplication tables, there are 7 split octonions (one for each of 7 triads in the parent octonion). This PDF is a comprehensive list of all 3840=480+3360 (octonions + split octonions), their Fano planes, and multiplication tables. They are organized in pairs of 240 parent octonions=(8-bit sign mask)*(30 canonical sets of 7 triads). The pairs of parent octonions are created by flipping (reversing) the first triad (center circular line) creating a unique Fano plane mnemonic.

Comments: 321 Pages.

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Submission history

[v1] 2015-03-28 15:32:12

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