S2:{6,6}

Statistics

genus c	2, orientable
Schläfli formula c	{6,6}
V / F / E c	2 / 2 / 6
notes
vertex, face multiplicity c	6, 6
Petrie polygons holes 2nd-order Petrie polygons 3rd-order holes 3rd-order Petrie polygons	6, each with 2 edges 2, each with 6 edges 6, each with 2 edges 6, each with 2 edges 6, each with 2 edges
antipodal sets	1 of ( 2v ), 1 of ( 2f ), 3 of ( 2e )
rotational symmetry group	C6×C2, with 12 elements
full symmetry group	D6×C2×C2, with 24 elements
its presentation c	< r, s, t | t2, sr2s, (r, s), (rt)2, (st)2, r6 >
C&D number c	R2.5
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 6-hosohedron.

It can be built by 2-splitting {3,6}_(1,1).

It can be rectified to give S2:{6,4}.

It can be derived by stellation (with path <1,-1;-1,1>) from {6,3}_(1,1). The density of the stellation is 4.

It is a member of series γ° .
It is a member of series ε .
It is a member of series ε' .

List of regular maps in orientable genus 2.

Wireframe constructions

	×	{6,3}(1,1)
	×	{6,3}(1,1)
	×	the 3-hosohedron

Underlying Graph

Its skeleton is 6 . K₂.

Other Regular Maps

General Index

Groups of order 4 6 8 9 10 12 14 15 16 18 20 21 22 24 25 27 28 30 48 60 120 168 336 360 720

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