S5:{4,12}

Statistics

genus c5, orientable
Schläfli formula c{4,12}
V / F / E c 4 / 12 / 24
notesreplete is not a polyhedral map permutes its vertices oddly
vertex, face multiplicity c6, 2
Petrie polygons
holes
2nd-order Petrie polygons
3rd-order holes
3rd-order Petrie polygons
4th-order holes
4th-order Petrie polygons
5th-order holes
5th-order Petrie polygons
6th-order holes
4, each with 12 edges
24, each with 2 edges
8, each with 6 edges
12, each with 4 edges
12, each with 4 edges
24, each with 2 edges
8 double, each with 6 edges
24, each with 2 edges
4, each with 12 edges
12, each with 4 edges
rotational symmetry group48 elements.
full symmetry group96 elements.
its presentation c< r, s, t | t2, r4, (rs)2, (rs‑1)2, (rt)2, (st)2, s12  >
C&D number cR5.7
The statistics marked c are from the published work of Professor Marston Conder.

Relations to other Regular Maps

Its dual is S5:{12,4}.

It can be 3-split to give R25.29.
It can be 5-split to give R45.28′.
It can be 7-split to give R65.126′.
It can be 9-split to give R85.52′.

It is a member of series m.

List of regular maps in orientable genus 5.

Underlying Graph

Its skeleton is 6 . 4-cycle.

Other Regular Maps

General Index

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