S3:{3,12}

Statistics

genus c3, orientable
Schläfli formula c{3,12}
V / F / E c 4 / 16 / 24
notesreplete is not a polyhedral map permutes its vertices evenly
vertex, face multiplicity c4, 1
Petrie polygons
holes
2nd-order Petrie polygons
3rd-order holes
3rd-order Petrie polygons
4th-order holes
4th-order Petrie polygons
5th-order holes
5th-order Petrie polygons
6th-order holes
6 -fold, each with 8 edges
4, each with 12 edges
6, each with 8 edges
12, each with 4 edges
24, each with 2 edges
4, each with 12 edges
4, each with 12 edges
8, each with 6 edges
6, each with 8 edges
24, each with 2 edges
antipodal sets8 of ( 2f ), 12 of ( 2e )
rotational symmetry groupC2 ↑ (A4,C2), with 48 elements
full symmetry group96 elements.
its presentation c< r, s, t | t2, r‑3, (rs)2, (rt)2, (st)2, srs‑2rs3 >
C&D number cR3.3
The statistics marked c are from the published work of Professor Marston Conder.

Relations to other Regular Maps

Its dual is S3:{12,3}.

Its Petrie dual is N16.7.

It can be 2-split to give R13.11.
It can be 4-split to give R33.70.

It can be rectified to give rectification of S3:{12,3}.

List of regular maps in orientable genus 3.

Underlying Graph

Its skeleton is 4 . K4.

Other Regular Maps

General Index

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