S5:{3,8}

Statistics

genus c5, orientable
Schläfli formula c{3,8}
V / F / E c 24 / 64 / 96
notesreplete singular
vertex, face multiplicity c1, 1
Petrie polygons
16, each with 12 edges
rotational symmetry group192 elements.
full symmetry group384 elements.
its presentation c< r, s, t | t2, r‑3, (rs)2, (rt)2, (st)2, s8, s2rs‑2r‑1sr‑1s‑1rs‑2rs2  >
C&D number cR5.1
The statistics marked c are from the published work of Professor Marston Conder.

Relations to other Regular Maps

Its dual is S5:{8,3}.

Its Petrie dual is N58.7′.

It is a 2-fold cover of S3:{3,8}.

It can be 2-split to give R41.26.

List of regular maps in orientable genus 5.

Comments

Its graph is the same as that of the 24-cell.

This regular map features in Jarke J. van Wijk's movie Symmetric Tiling of Closed Surfaces: Visualization of Regular Maps, 2:0 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