S2:{8,4}

Statistics

genus c2, orientable
Schläfli formula c{8,4}
V / F / E c 4 / 2 / 8
notesFaces share vertices with themselves is not a polyhedral map permutes its vertices oddly
vertex, face multiplicity c2, 8
Petrie polygons
holes
2 Eulerian, each with 8 edges
8, each with 2 edges
antipodal sets2 of ( 2v ), 1 of ( 2f ), 4 of ( 2e )
rotational symmetry groupquasidihedral(16), with 16 elements
full symmetry group32 elements.
its presentation c< r, s, t | t2, s4, (sr)2, (sr‑1)2, (st)2, (rt)2, r‑2s2r‑2 >
C&D number cR2.3′
The statistics marked c are from the published work of Professor Marston Conder.

Relations to other Regular Maps

Its dual is S2:{4,8}.

It is self-Petrie dual.

It can be 2-fold covered to give S3:{8,4|4}.
It can be 2-fold covered to give S3:{8,4|2}.

It can be 3-split to give S6:{24,4}.
It can be 5-split to give R10.12′.
It can be 7-split to give R14.5′.
It can be 9-split to give R18.3′.
It can be 11-split to give R22.6′.

It can be rectified to give rectification of S2:{8,4}.
It is the result of rectifying S2:{8,8}.

It can be derived by stellation (with path <>/2) from S2:{3,8}. The density of the stellation is 2.

It is a member of series j.

List of regular maps in orientable genus 2.

Wireframe constructions

p  {8,4}  2 | 4/4 | 4 × the hemi-4-hosohedron
t  {8,4}  2 | 4/4 | 4 × {4,4}(1,0) mo01:60,w09:12

Underlying Graph

Its skeleton is 2 . 4-cycle.

Comments

This regular map features in Jarke J. van Wijk's movie Symmetric Tiling of Closed Surfaces: Visualization of Regular Maps, 1:0 seconds from the start. It is shown as a "wireframe diagram", on 2-fold 1-cycle. The wireframe is arranged as the skeleton of {4,4}(1,0).


Other Regular Maps

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