The di-hexagon


genus c0, orientable
Schläfli formula c{6,2}
V / F / E c 6 / 2 / 6
notesVertices with < 3 edges trivial is not a polyhedral map permutes its vertices oddly
vertex, face multiplicity c1, 6
Petrie polygons
2, each with 6 edges
antipodal sets3 of ( 2v, 2e ), 1 of ( 2f )
rotational symmetry groupD12, with 12 elements
full symmetry groupD6×C2×C2, with 24 elements
its presentation c< r, s, t | r2, s2, t2, (rs)6, (st)2, (rt)2 >
C&D number cR0.n6′
The statistics marked c are from the published work of Professor Marston Conder.

Relations to other Regular Maps

Its dual is the 6-hosohedron.

It is self-Petrie dual.

It is a 2-fold cover of the hemi-di-hexagon.

It can be built by 2-splitting the di-triangle.

It can be rectified to give the 6-lucanicohedron.

It can be triambulated to give the octahedron.

List of regular maps in orientable genus 0.

Underlying Graph

Its skeleton is 6-cycle.

Cayley Graphs based in this Regular Map

Type I


Other Regular Maps

General Index

The images on this page are copyright © 2010 N. Wedd