S3:{3,7}

Statistics

genus c3, orientable
Schläfli formula c{3,7}
V / F / E c 24 / 56 / 84
notesreplete singular is a polyhedral map permutes its vertices evenly
vertex, face multiplicity c1, 1
Petrie polygons
holes
2nd-order Petrie polygons
3rd-order holes
3rd-order Petrie polygons
21, each with 8 edges
24, each with 7 edges
28, each with 6 edges
42, each with 4 edges
21, each with 8 edges
antipodal sets8 of ( 3v ), 28 of ( 2f ), 21 of ( 4e )
rotational symmetry groupPSL(2,7), with 168 elements
full symmetry groupPGL(2,7), with 336 elements
its presentation c< r, s, t | t2, r‑3, (rs)2, (rt)2, (st)2, s‑7, (rs‑2)4 >
C&D number cR3.1
The statistics marked c are from the published work of Professor Marston Conder.

Relations to other Regular Maps

Its dual is the Klein map, S3:{7,3}.

Its Petrie dual is N41.3′.

It can be 2-split to give R33.38.

It can be rectified to give the quasi-Klein map, S3:{7,3}.

It can be stellated (with path <>/2) to give R19.23 . The density of the stellation is 3.
It can be stellated (with path <1,-1>) to give R19.23 . The density of the stellation is 3.
It can be stellated (with path <2,-2>) to give R19.23 . The density of the stellation is 9.
It can be stellated (with path <>/3) to give R10.9 . The density of the stellation is unknown.

List of regular maps in orientable genus 3.

Underlying Graph

Its skeleton is 7-valent Klein graph.

Comments

This regular map is related to the small cubicuboctahedron and the group M24.


Other Regular Maps

General Index

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