S2:{4,8}

Statistics

genus c	2, orientable
Schläfli formula c	{4,8}
V / F / E c	2 / 4 / 8
notes
vertex, face multiplicity c	8, 2
Petrie polygons holes 2nd-order Petrie polygons 3rd-order holes 3rd-order Petrie polygons 4th-order holes 4th-order Petrie polygons	2, each with 8 edges 8, each with 2 edges 4, each with 4 edges 4, each with 4 edges 2, each with 8 edges 8, each with 2 edges 8, each with 2 edges
antipodal sets	1 of ( 2v ), 2 of ( 2f ), 4 of ( 2e )
rotational symmetry group	quasidihedral(16), with 16 elements
full symmetry group	32 elements.
its presentation c	< r, s, t | t2, r4, (rs)2, (rs‑1)2, (rt)2, (st)2, s‑2r2s‑2 >
C&D number c	R2.3
The statistics marked c are from the published work of Professor Marston Conder.

Relations to other Regular Maps

Its dual is S2:{8,4}.

Its Petrie dual is S3:{8,8}₄.

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

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

It is its own 3-hole derivative.

It can be derived by stellation (with path <1,-1>) from S2:{3,8}. The density of the stellation is 3.

It is a member of series h.

List of regular maps in orientable genus 2.

Wireframe constructions

	×	the hemi-4-hosohedron
	×	{4,4}(1,0)	mo01:50,w09:11

Underlying Graph

Its skeleton is 8 . K₂.

Comments

This regular map features in Jarke J. van Wijk's movie Symmetric Tiling of Closed Surfaces: Visualization of Regular Maps, 0:55 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