genus c4, non-orientable
Schläfli formula c{6,4}
V / F / E c 6 / 4 / 12
notesreplete is not a polyhedral map permutes its vertices oddly
vertex, face multiplicity c1, 2
Petrie polygons
8, each with 3 edges
6, each with 4 edges
antipodal sets3 of ( 2v, h ), 4 of ( f, 2p ), 6 of ( 2e )
rotational symmetry groupS4×C2, with 48 elements
full symmetry groupS4×C2, with 48 elements
its presentation c< r, s, t | t2, s4, (sr)2, (st)2, (rt)2, (sr‑2)2, r6, sr‑1s‑2r‑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:{4,6}3.

Its Petrie dual is the octahedron.

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

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

It is the full shuriken of the tetrahedron.

List of regular maps in non-orientable genus 4.

Underlying Graph

Its skeleton is K2,2,2.

Other Regular Maps

General Index

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