S3{12,12}

Statistics

genus c	3, orientable
Schläfli formula c	{12,12}
V / F / E c	1 / 1 / 6
notes
vertex, face multiplicity c	12, 12
Petrie polygons holes 2nd-order Petrie polygons 3rd-order holes 3rd-order Petrie polygons 4th-order holes 4th-order Petrie polygons 5th-order holes	6, each with 2 edges 4, each with 3 edges 6, each with 2 edges 3, each with 4 edges 6, each with 2 edges 2, each with 6 edges 6, each with 2 edges 6, each with 2 edges
antipodal sets	3 of ( 2e )
rotational symmetry group	C12, with 12 elements
full symmetry group	D24, with 24 elements
its presentation c	< r, s, t | r12, r5s‑1, t2, (rt)2 >
C&D number c	R3.12
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-12-hosohedron.

It can be rectified to give S3:{12,4}.

It can be derived by stellation (with path <2,3;3,2>) from {3,6}_(1,1). The density of the stellation is 6.

It is a member of series β° .

List of regular maps in orientable genus 3.

Wireframe constructions

	×	{3,6}(1,1)
	×	{3,6}(1,1)

Underlying Graph

Its skeleton is 6 . 1-cycle.

Other Regular Maps

General Index

The image on this page is copyright © 2010 N. Wedd