S4:{16,4}

Statistics

genus c	4, orientable
Schläfli formula c	{16,4}
V / F / E c	8 / 2 / 16
notes
vertex, face multiplicity c	2, 16
Petrie polygons holes 2nd-order Petrie polygons	2, each with 16 edges 16, each with 2 edges 16, each with 2 edges
rotational symmetry group	32 elements.
full symmetry group	64 elements.
its presentation c	< r, s, t | t2, s4, (sr)2, (sr‑1)2, (st)2, (rt)2, r‑4s2r‑4 >
C&D number c	R4.5′
The statistics marked c are from the published work of Professor Marston Conder.

Relations to other Regular Maps

Its dual is S4:{4,16}.

It is self-Petrie dual.

It can be 3-split to give R12.3′.
It can be 5-split to give R20.2′.
It can be 7-split to give R28.8′.
It can be 9-split to give R36.7′.
It can be 11-split to give R44.2′.

It is the result of rectifying S4:{16,16}.

It is a member of series j.

List of regular maps in orientable genus 4.

Wireframe construction

	×	S2:{8,8}

Underlying Graph

Its skeleton is 2 . 8-cycle.

Other Regular Maps

General Index

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