S5:{4,12}

Statistics

genus c	5, orientable
Schläfli formula c	{4,12}
V / F / E c	4 / 12 / 24
notes
vertex, face multiplicity c	6, 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 group	48 elements.
full symmetry group	96 elements.
its presentation c	< r, s, t | t2, r4, (rs)2, (rs‑1)2, (rt)2, (st)2, s12  >
C&D number c	R5.7
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.

Wireframe constructions

	×	the 6-hosohedron
	×	the 6-hosohedron
	×	S2:{6,6}

Underlying Graph

Its skeleton is 6 . 4-cycle.

Other Regular Maps

General Index

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