The hemi-cuboctahedron

Statistics

genus c	1, non-orientable
Schläfli formula c	{4,3}
V / F / E c	6 / 4+3 / 12
notes	This is not a regular map, it has faces of two kinds (it is quasiregular).
rotational symmetry group	S4, with 24 elements
full symmetry group	S4, with 24 elements
its presentation c	< r, s, t | r2, s2, t2, (rs)4, (st)3, (rt)2, (srst)2 >

Relations to other Regular Maps

It is the result of rectifying the hemioctahedron.
It is the result of rectifying the hemicube.

List of regular maps in non-orientable genus 1.

Comments

This can be immersed in 3-space as the tetrahemihexahedron or regular heptahedron, used as an example in chapter 2 of Proofs and Refutations by Imre Lakatos.

Other Regular Maps

General Index

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