The 5-hosohedron

Statistics

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
holes
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.

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

D10

Type IIa

C10

Type III

D20

Type IIIa

D20

Other Regular Maps

General Index

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