genus c3, orientable
Schläfli formula c{8,8}
V / F / E c 2 / 2 / 8
notesFaces share vertices with themselves is not a polyhedral map permutes its vertices oddly
vertex, face multiplicity c8, 8
Petrie polygons
2nd-order Petrie polygons
3rd-order holes
3rd-order Petrie polygons
4th-order holes
4th-order Petrie polygons
4, each with 4 edges
4, each with 4 edges
8, each with 2 edges
2, each with 8 edges
4, each with 4 edges
8, each with 2 edges
8, each with 2 edges
antipodal sets1 of ( 2v ), 1 of ( 2f ), 4 of ( 2e )
rotational symmetry groupmodular(16), with 16 elements
full symmetry group32 elements.
its presentation c< r, s, t | t2, s‑1r2s‑1, (rs)2, (r‑1t)2, (s‑1t)2 >
C&D number cR3.10
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 S2:{4,8}.

It is a 2-fold cover of S2:{8,8}.

It can be rectified to give S3:{8,4|4}.

It is its own 3-hole derivative.

It can be derived by stellation (with path <2,1;1,2>) from {4,4}(1,1). The density of the stellation is 6.

It is a member of series kt.

List of regular maps in orientable genus 3.

Wireframe construction

m  {8,8}  2/4 | 2/4 | 2 × the 4-hosohedron

Underlying Graph

Its skeleton is 8 . K2.

Other Regular Maps

General Index

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