S2:{8,8}

Statistics

genus c	2, orientable
Schläfli formula c	{8,8}
V / F / E c	1 / 1 / 4
notes
vertex, face multiplicity c	8, 8
Petrie polygons holes 2nd-order Petrie polygons 3rd-order holes 3rd-order Petrie polygons 4th-order Petrie polygons	4, each with 2 edges 2, each with 4 edges 4, each with 2 edges 1, with 8 edges 4, each with 2 edges 4, each with 2 edges
rotational symmetry group	C8, with 8 elements
full symmetry group	D16, with 16 elements
its presentation c	< r, s, t | t2, r3s‑1, sr2s, (r‑1t)2 >
C&D number c	R2.6
The statistics marked c are from the published work of Professor Marston Conder.

Relations to other Regular Maps

It is self-dual.

Its Petrie dual is the hemi-8-hosohedron.

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

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

It is its own 3-hole derivative.

It can be derived by stellation (with path <2,1;1,2>) from {4,4}_(1,0). The density of the stellation is 6.

It is a member of series β° .

List of regular maps in orientable genus 2.

Wireframe constructions

	×	{4,4}(1,0)
	×	{4,4}(1,0)
	×	{4,4}(1,0)

Underlying Graph

Its skeleton is 4 . 1-cycle.

Other Regular Maps

General Index

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