S3:{4,8|2}

Statistics

genus c3, orientable
Schläfli formula c{4,8}
V / F / E c 4 / 8 / 16
notesreplete is not a polyhedral map permutes its vertices oddly
vertex, face multiplicity c4, 2
Petrie polygons
holes
2nd-order Petrie polygons
3rd-order holes
3rd-order Petrie polygons
4th-order holes
4, each with 8 edges
16, each with 2 edges
8, each with 4 edges
8, each with 4 edges
4, each with 8 edges
16, each with 2 edges
antipodal sets2 of ( 2v ), 4 of ( 2f ), 8 of ( 2e )
rotational symmetry group32 elements.
full symmetry group64 elements.
its presentation c< r, s, t | t2, r4, (rs)2, (rs‑1)2, (rt)2, (st)2, s8 >
C&D number cR3.6
The statistics marked c are from the published work of Professor Marston Conder.

Relations to other Regular Maps

Its dual is S3:{8,4|2}.

Its Petrie dual is R5.13.

It is a 2-fold cover of S2:{4,8}.

It can be 3-split to give R15.13′.
It can be 5-split to give R27.6′.
It can be 7-split to give R39.6′.
It can be 9-split to give R51.20′.
It can be 11-split to give R63.8′.

It can be rectified to give rectification of S3:{8,4|2}.

It is a member of series m.

List of regular maps in orientable genus 3.

Wireframe constructions

pd  {4,8}  4/4 | 2 | 4 × the 4-hosohedron C.Séquin
qd  {4,8}  4/4 | 2 | 4 × the 4-hosohedron C.Séquin
td  {4,8}  4/4 | 2 | 4 × {4,4}(1,1)

Underlying Graph

Its skeleton is 4 . 4-cycle.

Other Regular Maps

General Index

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