The hemi-4-hosohedron

Statistics

genus c1, non-orientable
Schläfli formula c{2,4}
V / F / E c 1 / 2 / 2
notesFaces with < 3 edges Faces share vertices with themselves Vertices share edges with themselves trivial is not a polyhedral map permutes its vertices evenly
vertex, face multiplicity c4, 2
Petrie polygons
holes
2nd-order Petrie polygons
1, each with 4 edges
2, each with 2 edges
0.57142857142857, each with 7 edges
antipodal sets1 of ( 2f ), 1 of ( 2e, 2h2 )
rotational symmetry groupD8, with 8 elements
full symmetry groupD8, with 8 elements
its presentation c< r, s, t | r2, s2, t2, (rs)2, (st)2, (rt)2, rst >
C&D number cN1.n2
The statistics marked c are from the published work of Professor Marston Conder.

Relations to other Regular Maps

Its dual is the hemi-di-square.

Its Petrie dual is {4,4}(1,0).

It can be 2-fold covered to give the 4-hosohedron.

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

It can be truncated to give the hemicube.

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

It is the half shuriken of the 2-hosohedron.

It is a member of series β .
It is a member of series κ .
It is a member of series λ .

List of regular maps in non-orientable genus 1.

Underlying Graph

Its skeleton is 2 . 1-cycle.

Other Regular Maps

General Index

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

The image on this page is copyright © 2010 N. Wedd