This is the Harries graph. It is a graph with the minimum number of vertices such that each vertex is connected to 3 others and every cycle has length at least 10. Such graphs are called (3,10)-cages.

This is the Balaban 10-cage, the first known (3,10)-cage. An \((r,g)\)-cage is graph where every vertex has \(r\) neighbors, the shortest cycle has length at least \(g\), and the number of vertices is maximal given these constraints.