S2:{3,8}

Statistics

genus ^c	2, orientable
Schläfli formula ^c	{3,8}
V / F / E ^c	6 / 16 / 24
notes
vertex, face multiplicity ^c	2, 1
Petrie polygons holes 2nd-order Petrie polygons 3rd-order holes 3rd-order Petrie polygons 4th-order holes	4, each with 12 edges 6, each with 8 edges 6, each with 8 edges 8, each with 6 edges 4, each with 12 edges 24, each with 2 edges
antipodal sets	3 of ( 2v ), 4 of ( 4f ), 12 of ( 2e )
rotational symmetry group	GL(2,3), with 48 elements
full symmetry group	Tucker's group, with 96 elements
its presentation ^c	< r, s, t \| t², r^‑3, (rs)², (rt)², (st)², (rs^‑3)² >
C&D number ^c	R2.1
The statistics marked ^c are from the published work of Professor Marston Conder.

Relations to other Regular Maps

Its dual is S2:{8,3}.

Its Petrie dual is N16.7′.

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

It can be 2-split to give R11.6.
It can be 5-split to give R38.5′.
It can be 7-split to give R56.10′.
It can be 10-split to give R83.7′.
It can be 11-split to give R92.11′.

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

It can be obtained by triambulating S2:{6,4}.

Its 3-hole derivative is S6:{6,8}₁₂.

It can be stellated (with path <1,-1>) to give S2:{4,8} . The density of the stellation is 3.
It can be stellated (with path <>/2) to give S2:{8,4} . The multiplicity of the stellation is 3 and the total density is 3.

List of regular maps in orientable genus 2.

Underlying Graph

Its skeleton is 2 . K_2,2,2.

Comments

This regular map features in Jarke J. van Wijk's movie Symmetric Tiling of Closed Surfaces: Visualization of Regular Maps, 1:10 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.

Other Regular Maps

General Index