The 9-hosohedron


genus c0, orientable
Schläfli formula c{2,9}
V / F / E c 2 / 9 / 9
notesFaces with < 3 edges trivial is not a polyhedral map permutes its vertices oddly
vertex, face multiplicity c9, 1
Petrie polygons
2nd-order Petrie polygons
3rd-order holes
3rd-order Petrie polygons
4th-order holes
4th-order Petrie polygons
1, with 18 edges
9, each with 2 edges
1, with 18 edges
9, each with 2 edges
3, each with 6 edges
9, each with 2 edges
1, with 18 edges
antipodal sets1 of ( 2v ), 9 of ( f, e, h2, h3, h4 ), 3 of ( 2p3 )
rotational symmetry groupD18, with 18 elements
full symmetry groupD18×C2, with 36 elements
its presentation c< r, s, t | r2, s2, t2, (rs)2, (st)9, (rt)2 >
C&D number cR0.n9
The statistics marked c are from the published work of Professor Marston Conder.

Relations to other Regular Maps

Its dual is the di-nonagon.

Its Petrie dual is S4:{18,9}.

It can be rectified to give the 9-lucanicohedron.

It is its own 2-hole derivative.
It is its own 4-hole derivative.

List of regular maps in orientable genus 0.

Underlying Graph

Its skeleton is 9 . K2.

Cayley Graphs based in this Regular Map

Type II


Type IIa


Other Regular Maps

General Index

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