# 1-cycle

### Statistics

It has degree 2, with 1 vertices and 1 edges.
It has girth 1, diameter 0 and radius 0.
Its symmetry group has 2 elements.
It is not bipartite.
It is Hamiltonian.
It is symmetric.
It is 1-arc-transitive.

### Regular maps

1-cycle is the skeleton of the dimonogon
1-cycle is the skeleton of the hemi-2-hosohedron
1-cycle is the skeleton of the hemi-4-hosohedron with muliplicity 2
1-cycle is the skeleton of {4,4}(1,0) with muliplicity 2
1-cycle is the skeleton of {3,6}(1,1) with muliplicity 3
1-cycle is the skeleton of the hemi-6-hosohedron with muliplicity 3
1-cycle is the skeleton of S2:{8,8} with muliplicity 4
1-cycle is the skeleton of the hemi-8-hosohedron with muliplicity 4
1-cycle is the skeleton of S2:{5,10} with muliplicity 5
1-cycle is the skeleton of the hemi-10-hosohedron with muliplicity 5
1-cycle is the skeleton of S3{12,12} with muliplicity 6
1-cycle is the skeleton of the hemi-12-hosohedron with muliplicity 6
1-cycle is the skeleton of S3{7,14} with muliplicity 7
1-cycle is the skeleton of the hemi-14-hosohedron with muliplicity 7
1-cycle is the skeleton of S4:{16,16} with muliplicity 8
1-cycle is the skeleton of the hemi-di-16gon with muliplicity 8
1-cycle is the skeleton of S5:{20,20} with muliplicity 10
1-cycle is the skeleton of S6:{24,24} with muliplicity 12

### Dual graphs

1-cycle is the dual of K2 in the plane