S2:{4,6}

Statistics

genus c2, orientable
Schläfli formula c{4,6}
V / F / E c 4 / 6 / 12
notesreplete is not a polyhedral map permutes its vertices oddly
vertex, face multiplicity c3, 2
Petrie polygons
holes
2nd-order Petrie polygons
3rd-order holes
3rd-order Petrie polygons
2, each with 12 edges
12, each with 2 edges
4, each with 6 edges
6, each with 4 edges
6, each with 4 edges
antipodal sets2 of ( 2v ), 3 of ( 2f ), 6 of ( 2e )
rotational symmetry groupC3 ⋊ D8, with 24 elements
full symmetry group48 elements.
its presentation c< r, s, t | t2, r4, (rs)2, (rs‑1)2, (rt)2, (st)2, s6 >
C&D number cR2.2
The statistics marked c are from the published work of Professor Marston Conder.

Relations to other Regular Maps

Its dual is S2:{6,4}.

Its Petrie dual is S4:{12,6}.

It can be 2-fold covered to give S3:{4,6}.

It can be 3-split to give R10.17′.
It can be 5-split to give R18.4′.
It can be 7-split to give R26.7′.
It can be 9-split to give R34.8′.
It can be 11-split to give R42.4′.

It can be rectified to give cubohemioctahedron.

It is a member of series m.

List of regular maps in orientable genus 2.

Wireframe constructions

pd {4,6} 4/3 | 2 | 4 × the 3-hosohedron w09:6
qd {4,6} 4/3 | 2 | 4 × the 3-hosohedron
td {4,6} 4/3 | 2 | 4 × {6,3}(1,1)

Underlying Graph

Its skeleton is 3 . 4-cycle.

Other Regular Maps

General Index

Orientable
sphere | torus | 2 | 3 | 4 | 5 | 6 |
Non-orientable
projective plane | 4 | 5 | 6 | 7 |

The images on this page are copyright © 2010 N. Wedd