File:3-bit Walsh permutations; Cayley 136 421; 28 triples; Fano.svg

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The vertices are the same as in this representation of the Coxeter graph.

This is an abstraction of the Cayley graph with its 168 vertices and 168 directed and 84 undirected edges.

Each of the 28 vertices corresponds to 6 vertices in the Cayley graph, which are tuples with the same 3 elements.

Among the 3-subsets of a 7-set these are the 28 that do not correspond to the 7 edges of the Fano plane.

The red edges correspond to directed and the green edges correspond to undirected edges in the Cayley graph.

Vertices connected by green edges are horizontally mirrored.

Most edges contain between 1 and 3 thin lines, which indicate how many elements the two vertices have in common.

The two thick red edges connect disjoint sets.
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Watchduck
You can name the author as "T. Piesk", "Tilman Piesk" or "Watchduck".
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with number vertices

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current11:15, 22 August 2022Thumbnail for version as of 11:15, 22 August 2022861 × 817 (65 KB)Watchduck (talk | contribs)Uploaded own work with UploadWizard

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