The 4-hosohedron

Statistics

genus c0, orientable
Schläfli formula c{2,4}
V / F / E c 2 / 4 / 4
notesFaces with < 3 edges trivial is not a polyhedral map permutes its vertices oddly
vertex, face multiplicity c4, 1
Petrie polygons
holes
2nd-order Petrie polygons
2, each with 4 edges
4, each with 2 edges
4, each with 2 edges
antipodal sets1 of ( 2v ), 2 of ( 2f ), 2 of ( 2e, 2h2 ), 1 of ( 2p1 )
rotational symmetry groupD8, with 8 elements
full symmetry groupD8×C2, with 16 elements
its presentation c< r, s, t | r2, s2, t2, (rs)2, (st)4, (rt)2 >
C&D number cR0.n4
The statistics marked c are from the published work of Professor Marston Conder.

Relations to other Regular Maps

Its dual is the di-square.

Its Petrie dual is {4,4}(1,1).

It is a 2-fold cover of the hemi-4-hosohedron.

It can be rectified to give the 4-lucanicohedron.
It is the result of rectifying the 2-hosohedron.

It can be truncated to give the cube.

It can be pyritified (type 2/4/3/4) to give the octahedron.

Its half shuriken is the hemi-8-hosohedron.

It is a member of series γ .
It is a member of series ζ' .
It is a member of series ζ°' .
It is a member of series μ .

List of regular maps in orientable genus 0.

Wireframe constructions

p {2,4} 2 | 4/1 | 4 × the 1-hosohedron
q {2,4} 2 | 4/1 | 4 × the 1-hosohedron
r {2,4} 2 | 4/1 | 4 × the 1-hosohedron
t {2,4} 2 | 4/1 | 4 × the 1-hosohedron

Underlying Graph

Its skeleton is 4 . K2.

Cayley Graphs based in this Regular Map


Type III

D8×C2

Type IIIa

D16

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