The hemi-6-hosohedron

Statistics

genus c1, non-orientable
Schläfli formula c{2,6}
V / F / E c 1 / 3 / 3
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 c6, 1
Petrie polygons
holes
2nd-order Petrie polygons
3rd-order holes
2, each with 3 edges
3, each with 2 edges
1, with 6 edges
3, each with 2 edges
antipodal sets3 of ( f, e, h2, h3 )
rotational symmetry groupD12, with 12 elements
full symmetry groupD12, with 12 elements
its presentation c< r, s, t | r2, s2, t2, (rs)2, (st)1, (rt)2 >
C&D number cN1.n3
The statistics marked c are from the published work of Professor Marston Conder.

Relations to other Regular Maps

Its dual is the hemi-di-hexagon.

Its Petrie dual is {3,6}(1,1).

It can be 2-fold covered to give the 6-hosohedron.

It can be rectified to give the hemi-6-lucanicohedron.

It is the half shuriken of the 3-hosohedron.

List of regular maps in non-orientable genus 1.

Underlying Graph

Its skeleton is 3 . 1-cycle.

Other Regular Maps

General Index

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