S2:{6,4}

Statistics

genus c2, orientable
Schläfli formula c{6,4}
V / F / E c 6 / 4 / 12
notesreplete is not a polyhedral map permutes its vertices oddly
vertex, face multiplicity c2, 3
Petrie polygons
holes
2nd-order Petrie polygons
2, each with 12 edges
12, each with 2 edges
12, each with 2 edges
antipodal sets3 of ( 2v ), 2 of ( 2f ), 6 of ( 2e ), 3 of ( 2h )
rotational symmetry groupC3 ⋊ D8, with 24 elements
full symmetry group48 elements.
its presentation c< r, s, t | t2, s4, (sr)2, (sr‑1)2, (st)2, (rt)2, r6 >
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:{4,6}.

Its Petrie dual is S3:{12,4}.

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

It can be 5-split to give R14.4′.
It can be 7-split to give R20.1′.
It can be 11-split to give R32.1′.

It can be rectified to give cubohemioctahedron.
It is the result of rectifying S2:{6,6}.

It can be triambulated to give S2:{3,8}.

It is a member of series l.

List of regular maps in orientable genus 2.

Wireframe constructions

p {6,4} 2 | 4/3 | 4 × the 3-hosohedron w09:7
q {6,4} 2 | 4/3 | 4 × the 3-hosohedron
t {6,4} 2 | 4/3 | 4 × {6,3}(1,1)

Underlying Graph

Its skeleton is 2 . 6-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