S3:{8,8}₂

Statistics

genus c	3, orientable
Schläfli formula c	{8,8}
V / F / E c	2 / 2 / 8
notes
vertex, face multiplicity c	8, 8
Petrie polygons holes 2nd-order Petrie polygons 3rd-order holes 3rd-order Petrie polygons 4th-order holes 4th-order Petrie polygons	8, each with 2 edges 4, each with 4 edges 8, each with 2 edges 2, each with 8 edges 8, each with 2 edges 8, each with 2 edges 8, each with 2 edges
antipodal sets	1 of ( 2v ), 1 of ( 2f ), 4 of ( 2e )
rotational symmetry group	C8×C2, with 16 elements
full symmetry group	D16×C2, with 32 elements
its presentation c	< r, s, t | t2, sr2s, (r, s), (rt)2, (st)2, r8 >
C&D number c	R3.11
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 8-hosohedron.

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

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

It is its own 3-hole derivative.

It is a member of series γ° .

List of regular maps in orientable genus 3.

Wireframe constructions

	×	{4,4}(1,1)
	×	{4,4}(1,1)
	×	{4,4}(1,1)
	×	the 4-hosohedron

Underlying Graph

Its skeleton is 8 . K₂.

Other Regular Maps

General Index

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