# 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 K_{2} in the plane

Lists of Graphs

Index to Regular Maps