S6:{24,4}

Statistics

genus c6, orientable
Schläfli formula c{24,4}
V / F / E c 12 / 2 / 24
notesFaces share vertices with themselves is not a polyhedral map permutes its vertices oddly
vertex, face multiplicity c2, 24
Petrie polygons
holes
2nd-order Petrie polygons
2, each with 24 edges
24, each with 2 edges
24, each with 2 edges
rotational symmetry group48 elements.
full symmetry group96 elements.
its presentation c< r, s, t | t2, s4, (sr)2, (sr‑1)2, (st)2, (rt)2, r6s2r6  >
C&D number cR6.5′
The statistics marked c are from the published work of Professor Marston Conder.

Relations to other Regular Maps

Its dual is S6:{4,24}.

It is self-Petrie dual.

It can be 5-split to give R30.3′.
It can be 7-split to give R42.3′.
It can be 11-split to give R66.5′.
It can be built by 3-splitting S2:{8,4}.

It is the result of rectifying S6:{24,24}.

It is a member of series η'.

List of regular maps in orientable genus 6.

Wireframe construction

p {24,4} 2 | 4/12 | 4 × the hemi-12-hosohedron

Underlying Graph

Its skeleton is 2 . 12-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