S5:{12,12}

Statistics

genus c5, orientable
Schläfli formula c{12,12}
V / F / E c 2 / 2 / 12
notesFaces share vertices with themselves trivial is not a polyhedral map permutes its vertices oddly
vertex, face multiplicity c12, 12
Petrie polygons
holes
2nd-order Petrie polygons
3rd-order holes
3rd-order Petrie polygons
12, each with 2 edges
4, each with 6 edges
12, each with 2 edges
6, each with 4 edges
12, each with 2 edges
rotational symmetry groupC12×C2, with 24 elements
full symmetry groupD24×C2, with 48 elements
its presentation c< r, s, t | t2, sr2s, (r, s), (rt)2, (st)2, r2tsr‑7str  >
C&D number cR5.15
The statistics marked c are from the published work of Professor Marston Conder.

Relations to other Regular Maps

It is self-dual.

Its Petrie dual is the 12-hosohedron.

It can be rectified to give S5:{12,4}.

It is a member of series k.

List of regular maps in orientable genus 5.

Wireframe constructions

m  {12,12}  2/6 | 2/6 | 2 × S2:{6,6} unconfirmed
x  {10,10}  2/5 | 2/5 | 2 × S2:{6,6} unconfirmed
y  {10,10}  2/5 | 2/5 | 2 × S2:{6,6}
z  {12,12}  2/6 | 2/6 | 2 × the 6-hosohedron

Underlying Graph

Its skeleton is 12 . K2.

Other Regular Maps

General Index

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