genus c5, orientable
Schläfli formula c{5,4}
V / F / E c 40 / 32 / 80
notesreplete singular
vertex, face multiplicity c1, 1
Petrie polygons
16, each with 10 edges
rotational symmetry group160 elements.
full symmetry group320 elements.
its presentation c< r, s, t | t2, s4, (sr)2, (st)2, (rt)2, r‑5, (sr‑1)4  >
C&D number cR5.3′
The statistics marked c are from the published work of Professor Marston Conder.

Relations to other Regular Maps

Its dual is S5:{4,5}.

It is a 2-fold cover of C6:{5,4}.

It can be 2-split to give R25.7′.
It can be 3-split to give R45.5′.

List of regular maps in orientable genus 5.


This regular map features in Jarke J. van Wijk's movie Symmetric Tiling of Closed Surfaces: Visualization of Regular Maps, 2:30 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