S5:{4,5}

Statistics

genus c	5, orientable
Schläfli formula c	{4,5}
V / F / E c	32 / 40 / 80
notes
vertex, face multiplicity c	1, 1
Petrie polygons	16, each with 10 edges
rotational symmetry group	160 elements.
full symmetry group	320 elements.
its presentation c	< r, s, t | t2, r4, (rs)2, (rt)2, (st)2, s‑5, (rs‑1)4  >
C&D number c	R5.3
The statistics marked c are from the published work of Professor Marston Conder.

Relations to other Regular Maps

Its dual is S5:{5,4}.

Its Petrie dual is R17.18′.

It is a 2-fold cover of N6:{4,5}.

List of regular maps in orientable genus 5.

Underlying Graph

Its skeleton is 5-cube.

Comments

This regular map features in Jarke J. van Wijk's movie Symmetric Tiling of Closed Surfaces: Visualization of Regular Maps, 2:20 seconds from the start. It is shown as a "wireframe diagram", on 2-fold 4-cycle. The wireframe is arranged as the skeleton of {4,4}_(2,0).

Other Regular Maps

General Index