The hemioctahedron


genus c1, non-orientable
Schläfli formula c{3,4}
V / F / E c 3 / 4 / 6
notesreplete singular is not a polyhedral map permutes its vertices oddly cantankerous
vertex, face multiplicity c2, 1
Petrie polygons
2nd-order Petrie polygons
4, each with 3 edges
3, each with 4 edges
3, each with 4 edges
antipodal sets4 of ( f, p1 ), 3 of ( 2e ), 3 of ( 2h2 )
rotational symmetry groupS4, with 24 elements
full symmetry groupS4, with 24 elements
its presentation c< r, s, t | r2, s2, t2, (rs)3, (st)4, (rt)2, (srst)2 >
C&D number cN1.1
The statistics marked c are from the published work of Professor Marston Conder.

Relations to other Regular Maps

Its dual is the hemicube.

It is self-Petrie dual.

It can be 2-fold covered to give the octahedron.

It can be 2-split to give C4:{6,4}6.

It can be rectified to give the hemi-cuboctahedron.

It is the result of pyritifying (type 2/4/3/4) the hemi-4-hosohedron.

List of regular maps in non-orientable genus 1.

Underlying Graph

Its skeleton is 2 . K3.

Other Regular Maps

General Index

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