The hemioctahedron

Statistics

genus c	1, non-orientable
Schläfli formula c	{3,4}
V / F / E c	3 / 4 / 6
notes
vertex, face multiplicity c	2, 1
Petrie polygons holes 2nd-order Petrie polygons	4, each with 3 edges 3, each with 4 edges 3, each with 4 edges
antipodal sets	4 of ( f, p1 ), 3 of ( 2e ), 3 of ( 2h2 )
rotational symmetry group	S4, with 24 elements
full symmetry group	S4, with 24 elements
its presentation c	< r, s, t | r2, s2, t2, (rs)3, (st)4, (rt)2, (srst)2 >
C&D number c	N1.1
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 N4:{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