The hemicube


genus c1, non-orientable
Schläfli formula c{4,3}
V / F / E c 4 / 3 / 6
notesreplete singular is not a polyhedral map permutes its vertices oddly
vertex, face multiplicity c1, 2
Petrie polygons
4, each with 3 edges
antipodal sets4 of ( v, p1 ), 3 of ( 2e ), 3 of ( f )
rotational symmetry groupS4, with 24 elements
full symmetry groupS4, with 24 elements
its presentation c< r, s, t | r2, s2, t2, (rs)4, (st)3, (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 hemioctahedron.

Its Petrie dual is the tetrahedron.

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

It can be rectified to give the hemi-cuboctahedron.

It can be obtained by truncating the hemi-4-hosohedron.

It can be pyritified (type 4/3/5/3) to give the hemidodecahedron.

Its full shuriken is C5:{8,4}.
Its stretched half shuriken is C5:{12,3}.

List of regular maps in non-orientable genus 1.

Underlying Graph

Its skeleton is K4.

Other Regular Maps

General Index

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