cubic distance-regular graph with 28 vertices and 42 edges
Coxeter graph
aeb.win.tue.nl →This is the graph on the triangles in the Fano plane, where triangles are adjacent when they are disjoint. The Coxeter graph is maximally non-Hamiltonian: there is a Hamiltonian path between any two nonadjacent vertices. The girth is 7. The binary code generated by the cycles has parameters [42,15,7], with weight enumerator
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Discovered by embedding cosine similarity (sentence-transformers MiniLM, 384-dim).