Perkel graph

In mathematics, the Perkel graph, named after Manley Perkel, is a 6-regular graph with 57 vertices and 171 edges. It is the unique distance-regular graph with intersection array (6, 5, 2; 1, 1, 3).^[1] The Perkel graph is also distance-transitive.

Perkel graph
Perkel graphs with 19-fold symmetry
Vertices	57
Edges	171
Radius	3
Diameter	3
Girth	5
Automorphisms	3420
Chromatic number	3
Properties	Regular, distance-transitive
Table of graphs and parameters

It is also the skeleton of an abstract regular polytope, the 57-cell.

The vertex set is Z₃ × Z₁₉ where (i,j) is joined to (i+1,k) when (k-j)³ = 2⁶ⁱ.