The 8-hosohedron


genus c0, orientable
Schläfli formula c{2,8}
V / F / E c 2 / 8 / 8
notesFaces with < 3 edges trivial is not a polyhedral map permutes its vertices oddly
vertex, face multiplicity c8, 1
Petrie polygons
2nd-order Petrie polygons
3rd-order holes
3rd-order Petrie polygons
4th-order holes
4th-order Petrie polygons
2, each with 8 edges
8, each with 2 edges
4, each with 4 edges
8, each with 2 edges
2, each with 8 edges
8, each with 2 edges
8, each with 2 edges
antipodal sets1 of ( 2v ), 4 of ( 2f, 2h3 ), 4 of ( 2e, 2h2, 2h4 ), 1 of ( 2p1, 2p3 )1 of ( 2p2 )
rotational symmetry groupD16, with 16 elements
full symmetry groupD16×C2, with 32 elements
its presentation c< r, s, t | r2, s2, t2, (rs)2, (st)8, (rt)2 >
C&D number cR0.n8
The statistics marked c are from the published work of Professor Marston Conder.

Relations to other Regular Maps

Its dual is the di-octagon.

Its Petrie dual is S3:{8,8}2.

It is a 2-fold cover of the hemi-8-hosohedron.

It can be rectified to give the 8-lucanicohedron.

It is its own 3-hole derivative.

List of regular maps in orientable genus 0.

Underlying Graph

Its skeleton is 8 . 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