S5:{6,4}

Statistics

genus c	5, orientable
Schläfli formula c	{6,4}
V / F / E c	24 / 16 / 48
notes
vertex, face multiplicity c	1, 1
Petrie polygons	8, each with 12 edges
rotational symmetry group	96 elements.
full symmetry group	192 elements.
its presentation c	< r, s, t | t2, s4, (sr)2, (st)2, (rt)2, r6, (sr‑1)4, rsr‑2s2r3s‑1  >
C&D number c	R5.4′
The statistics marked c are from the published work of Professor Marston Conder.

Relations to other Regular Maps

Its dual is S5:{4,6}.

Its Petrie dual is R9.9′.

It can be 5-split to give R53.1′.
It can be 7-split to give R77.1′.

It is the result of rectifying S5:{6,6}.

List of regular maps in orientable genus 5.

Wireframe construction

	×	the cube	mo01:130,w09:18

Comments

This regular map features in Jarke J. van Wijk's movie Symmetric Tiling of Closed Surfaces: Visualization of Regular Maps, 2:10 seconds from the start. It is shown as a "wireframe diagram", on cube. The wireframe is arranged as the skeleton of the cube.

Other Regular Maps

General Index