It has degree 3, with 112 vertices and 168 edges.
It has girth 10, diameter 8 and radius 7.
Its symmetry group is PSL(2,7), with 168 elements.
It is bipartite.
It is Hamiltonian.
It is semi-symmetric.
https://en.wikipedia.org/wiki/Ljubljana_graph
For copyright details of Wikipedia images see Ljubljana_graph_--_Heawood_representation.jpg Ljubljana_graph_hamiltonian.svg.