genus c4, non-orientable
Schläfli formula c{4,6}
V / F / E c 4 / 6 / 12
notesreplete is not a polyhedral map permutes its vertices oddly
vertex, face multiplicity c2, 1
Petrie polygons
2nd-order Petrie polygons
3rd-order holes
8, each with 3 edges
6 Hamiltonian, each with 4 edges
4, each with 6 edges
12, each with 2 edges
antipodal sets4 of ( v, 2p, p2 ), 3 of ( 2f ), 6 of ( 2e, 2h3 )
rotational symmetry groupS4×C2, with 48 elements
full symmetry groupS4×C2, with 48 elements
its presentation c< r, s, t | t2, r4, (rs)2, (rt)2, (st)2, (rs‑2)2, s6, rs‑1r‑2s‑2t >
C&D number cN4.2
The statistics marked c are from the published work of Professor Marston Conder.

Relations to other Regular Maps

Its dual is C4:{6,4}3.

Its Petrie dual is {3,6}(2,2).

It can be 2-fold covered to give S3:{4,6}.

It can be rectified to give rectification of C4:{6,4}3.

It is the half shuriken of the cube.

List of regular maps in non-orientable genus 4.

Underlying Graph

Its skeleton is 2 . K4.

Other Regular Maps

General Index

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