S3{12,12}

Statistics

genus c3, orientable
Schläfli formula c{12,12}
V / F / E c 1 / 1 / 6
notesFaces share vertices with themselves Faces share edges with themselves Vertices share edges with themselves trivial is not a polyhedral map permutes its vertices evenly
vertex, face multiplicity c12, 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 sets3 of ( 2e )
rotational symmetry groupC12, with 12 elements
full symmetry groupD24, with 24 elements
its presentation c< r, s, t | r12, r5s‑1, t2, (rt)2 >
C&D number cR3.12
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 s.

List of regular maps in orientable genus 3.

Underlying Graph

Its skeleton is 6 . 1-cycle.

Other Regular Maps

General Index

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