The dual Klein map

Statistics

genus ^c	3, orientable
Schläfli formula ^c	{3,7}
V / F / E ^c	24 / 56 / 84
notes
vertex, face multiplicity ^c	1, 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 sets	8 of ( 3v ), 28 of ( 2f ), 21 of ( 4e )
rotational symmetry group	PSL(2,7), with 168 elements
full symmetry group	PSL(2,7)×C2, 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 ^c	R3.1
The statistics marked ^c are from the published work of Professor Marston Conder.

Relations to other Regular Maps

Its dual is the Klein map.

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.

Its 2-hole derivative is R19.23.
Its 3-hole derivative is R10.9.

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.

For a version of the diagram with the vertices labelled as in the "roadmap", click here.

Other Regular Maps

General Index