Following my post on Topology meets Keyboard Design, I spent a few days exploring small less symmetric graphs, trying to find something in the region of 30~42 edges, 20~29 vertices, and as good a girth as possible (especially to have better rollover for the modifier & layer keys) for use in an ergonomic keyboard design. Then I realised as a starting point we can just use part of the 30 vertex Tutte-Coxeter graph, and get 6-key rollover automatically.
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All 30 vertices in Tutte-Coxeter graph | 28 of 30 vertices in Tutte-Coxeter graph | 26 of 30 vertices in Tutte-Coxeter graph |