S4:{3,12}

Statistics

genus c4, orientable
Schläfli formula c{3,12}
V / F / E c 6 / 24 / 36
notesreplete is not a polyhedral map permutes its vertices oddly
vertex, face multiplicity c3, 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
12 Hamiltonian, each with 6 edges
6, each with 12 edges
18, each with 4 edges
24, each with 3 edges
12 Hamiltonian, each with 6 edges
12 double, each with 6 edges
36, each with 2 edges
24, each with 3 edges
12 Hamiltonian, each with 6 edges
18, each with 4 edges
rotational symmetry group72 elements.
full symmetry group144 elements.
its presentation c< r, s, t | t2, r‑3, (rs)2, (rt)2, (st)2, (sr‑1s)3, srs‑3rs4 >
C&D number cR4.1
The statistics marked c are from the published work of Professor Marston Conder.

Relations to other Regular Maps

Its dual is S4:{12,3}.

Its Petrie dual is N20.3.

It can be 2-split to give R19.18.
It can be 4-split to give R49.67.
It can be 5-split to give R64.27′.
It can be 7-split to give R94.10′.

It can be obtained by triambulating S4:{6,6}3,2.

It can be stellated (with path <1,-1>) to give S4:{6,12} . The density of the stellation is 3.

List of regular maps in orientable genus 4.

Underlying Graph

Its skeleton is 3 . K2,2,2.

Comments

The 4th-order holes have six edges, but involve only three distinct edges and two distinct vertices.


Other Regular Maps

General Index

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