The 6-hosohedron


genus c0, orientable
Schläfli formula c{2,6}
V / F / E c 2 / 6 / 6
notesFaces with < 3 edges trivial is not a polyhedral map permutes its vertices oddly
vertex, face multiplicity c6, 1
Petrie polygons
2nd-order Petrie polygons
3rd-order holes
3rd-order Petrie polygons
2, each with 6 edges
6, each with 2 edges
2, each with 6 edges
6, each with 2 edges
6, each with 2 edges
antipodal sets1 of ( 2v ), 3 of ( 2f, 2h3 ), 3 of ( 2e, 2h2 ), 1 of ( 2p1 ), 1 of ( 2p2 )
rotational symmetry groupD12, with 12 elements
full symmetry groupD6×C2×C2, with 24 elements
its presentation c< r, s, t | r2, s2, t2, (rs)2, (st)6, (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 di-hexagon.

Its Petrie dual is S2:{6,6}.

It is a 2-fold cover of the hemi-6-hosohedron.

It can be rectified to give the 6-lucanicohedron.

Its half shuriken is the hemi-12-hosohedron.

List of regular maps in orientable genus 0.

Underlying Graph

Its skeleton is 6 . K2.

Cayley Graphs based in this Regular Map

Type II


Type IIa


Type III


Type IIIa


Other Regular Maps

General Index

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