The 5-hosohedron


genus c0, orientable
Schläfli formula c{2,5}
V / F / E c 2 / 5 / 5
notesFaces with < 3 edges trivial is not a polyhedral map permutes its vertices oddly
vertex, face multiplicity c5, 1
Petrie polygons
2nd-order Petrie polygons
1, with 10 edges
5, each with 2 edges
1, with 10 edges
antipodal sets1 of ( 2v ), 5 of ( f, e, h2 )
rotational symmetry groupD10, with 10 elements
full symmetry groupD20, with 20 elements
its presentation c< r, s, t | r2, s2, t2, (rs)2, (st)5, (rt)2 >
C&D number cR0.n5
The statistics marked c are from the published work of Professor Marston Conder.

Relations to other Regular Maps

Its dual is the di-pentagon.

Its Petrie dual is S2:{10,5}.

It can be rectified to give the 5-lucanicohedron.

It is its own 2-hole derivative.

Its half shuriken is the hemi-10-hosohedron.

List of regular maps in orientable genus 0.

Underlying Graph

Its skeleton is 5 . 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