S5:{12,12}

Statistics

genus c	5, orientable
Schläfli formula c	{12,12}
V / F / E c	2 / 2 / 12
notes
vertex, face multiplicity c	12, 12
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 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 4, each with 6 edges 12, each with 2 edges 2, each with 12 edges 12, each with 2 edges 12, each with 2 edges
rotational symmetry group	C12×C2, with 24 elements
full symmetry group	D24×C2, with 48 elements
its presentation c	< r, s, t | t2, sr2s, (r, s), (rt)2, (st)2, r2tsr‑7str  >
C&D number c	R5.15
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 its own 5-hole derivative.

It is a member of series k.

List of regular maps in orientable genus 5.

Wireframe constructions

	×	S2:{6,6}		unconfirmed
	×	S2:{6,6}		unconfirmed
	×	S2:{6,6}
	×	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