Perkel graph

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Perkel graph: A 6-regular, distance-regular graph with 57 vertices and 171 edges. It is distance-transitive and serves as the skeleton of the regular 57-cell, a 4-dimensional polytope. The graph has radius 3, diameter 3, and girth 5. It has 3,420 automorphisms and chromatic number 3. Its vertices are pairs (i, j) from Z3 × Z19, and two vertices (i, j) and (i+1, k) are connected if (k − j)^3 ≡ 26 i (mod 19).