genus c2, orientable
Schläfli formula c{8,3}
V / F / E c 16 / 6 / 24
notesreplete is not a polyhedral map permutes its vertices evenly
vertex, face multiplicity c1, 2
Petrie polygons
4, each with 12 edges
antipodal sets4 of ( 4v ), 3 of ( 2f ), 12 of ( 2e )
rotational symmetry groupGL(2,3), with 48 elements
full symmetry groupTucker's group, with 96 elements
its presentation c< r, s, t | t2, s‑3, (sr)2, (st)2, (rt)2, (sr‑3)2 >
C&D number cR2.1′
The statistics marked c are from the published work of Professor Marston Conder.

Relations to other Regular Maps

Its dual is S2:{3,8}.

Its Petrie dual is S3:{12,3}.

It can be 2-fold covered to give the Dyck map.

It can be rectified to give rectification of S2:{8,3}.

List of regular maps in orientable genus 2.

Underlying Graph

Its skeleton is Möbius-Kantor graph.


This regular map features in Jarke J. van Wijk's movie Symmetric Tiling of Closed Surfaces: Visualization of Regular Maps, 1:20 seconds from the start. It is shown as a "wireframe diagram", on 3-fold K2. The wireframe is arranged as the skeleton of the 3-hosohedron.

Cayley Graphs based in this Regular Map

Type I


Type II


Type IIa


Other Regular Maps

General Index

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