# 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 polygonsholes2nd-order Petrie polygons3rd-order holes3rd-order Petrie polygons4th-order holes 4, each with 12 edges6, each with 8 edges6, each with 8 edges8, each with 6 edges4, each with 12 edges24, 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.

### Underlying Graph

Its skeleton is 2 . K2,2,2.

General Index 