S3:{8,4|2}

Statistics

genus c3, orientable
Schläfli formula c{8,4}
V / F / E c 8 / 4 / 16
notesreplete is not a polyhedral map permutes its vertices oddly
vertex, face multiplicity c2, 4
Petrie polygons
holes
4, each with 8 edges
16, each with 2 edges
antipodal sets4 of ( 2v ), 2 of ( 2f ), 8 of ( 2e )
rotational symmetry group32 elements.
full symmetry group64 elements.
its presentation c< r, s, t | t2, s4, (sr)2, (sr‑1)2, (st)2, (rt)2, r8 >
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:{4,8|2}.

It is self-Petrie dual.

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

It can be 3-split to give R11.3′.
It can be 5-split to give R19.10′.
It can be 7-split to give R27.2′.
It can be 9-split to give R35.1′.
It can be 11-split to give R43.5′.

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

It is a member of series l.

List of regular maps in orientable genus 3.

Wireframe constructions

p {8,4} 2 | 4/4 | 4 × the 4-hosohedron C.Séquin
q {8,4} 2 | 4/4 | 4 × the 4-hosohedron C.Séquin
t {8,4} 2 | 4/4 | 4 × {4,4}(1,1)

Underlying Graph

Its skeleton is 2 . 8-cycle.

Other Regular Maps

General Index

Orientable
sphere | torus | 2 | 3 | 4 | 5 | 6 |
Non-orientable
projective plane | 4 | 5 | 6 | 7 |

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