It has degree 2, with 12 vertices and 12 edges.
It has girth 12, diameter 6 and radius 6.
Its symmetry group has 24 elements.
It is bipartite.
It is Hamiltonian.
It is symmetric.
It is 11-arc-transitive.
12-cycle is the skeleton of the di-dodecagon
12-cycle is the skeleton of the hemi-di-24gon
12-cycle is the skeleton of S5:{12,4} with muliplicity 2
12-cycle is the skeleton of S6:{24,4} with muliplicity 2