The 2-hosohedron

Statistics

genus c0, orientable
Schläfli formula c{2,2}
V / F / E c 2 / 2 / 2
notesFaces with < 3 edges Vertices with < 3 edges trivial is not a polyhedral map permutes its vertices oddly
vertex, face multiplicity c2, 2
Petrie polygons
2, each with 2 edges
antipodal sets1 of ( 2v ), 1 of ( 2f ), 1 of ( 2e )
rotational symmetry groupC2×C2, with 4 elements
full symmetry groupC2×C2×C2, with 8 elements
its presentation c< r, s, t | r2, s2, t2, (rs)2, (st)2, (rt)2 >
C&D number cR0.n2
The statistics marked c are from the published work of Professor Marston Conder.

Relations to other Regular Maps

It is self-dual.

It is self-Petrie dual.

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

It can be built by 2-splitting the dimonogon.

It can be rectified to give the 4-hosohedron.

It is the diagonalisation of the 1-hosohedron.

Its half shuriken is the hemi-4-hosohedron.

It is a member of series k.

List of regular maps in orientable genus 0.

Wireframe constructions

w {2,2} 2/1 | 2/1 | 2 × the 1-hosohedron
x {2,2} 2/1 | 2/1 | 2 × the 1-hosohedron
y {4,4} 2/2 | 2/2 | 2 × the 1-hosohedron
z {2,2} 2/1 | 2/1 | 2 × the 1-hosohedron

Underlying Graph

Its skeleton is 2 . K2.

Cayley Graphs based in this Regular Map


Type II

C2×C2

Other Regular Maps

General Index

Orientable
sphere | torus | 2 | 3 | 4 | 5 | 6 |
Non-orientable
projective plane | 4 | 5 | 6 | 7 |

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