S4:{4,6}

Statistics

genus c4, orientable
Schläfli formula c{4,6}
V / F / E c 12 / 18 / 36
notesreplete singular is not a polyhedral map permutes its vertices oddly
vertex, face multiplicity c1, 1
Petrie polygons
holes
2nd-order Petrie polygons
3rd-order holes
18, each with 4 edges
12, each with 6 edges
12, each with 6 edges
18, each with 4 edges
antipodal sets9 of ( 2v ), 6 of ( 2f ), 18 of ( 2e ), 9 of ( 2h ), 6 of ( 2p2 )
rotational symmetry group72 elements.
full symmetry group144 elements.
its presentation c< r, s, t | t2, r4, (rs)2, (rt)2, (st)2, s6, srs‑1r2s‑1rs >
C&D number cR4.3
The statistics marked c are from the published work of Professor Marston Conder.

Relations to other Regular Maps

Its dual is S4:{6,4}.

It is a 2-fold cover of C5:{4,6}.

It can be 5-split to give R52.5′.
It can be 7-split to give R76.13′.

List of regular maps in orientable genus 4.

Wireframe construction

rd  {4,6}  4/3 | 2 | 4 × {6,3}(0,2) C.Séquin

Underlying Graph

Its skeleton is K6,6.

Other Regular Maps

General Index

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