S2:{8,8}

Statistics

genus c2, orientable
Schläfli formula c{8,8}
V / F / E c 1 / 1 / 4
notesFaces share vertices with themselves Faces share edges with themselves Vertices share edges with themselves is not a polyhedral map trivial permutes its vertices evenly
vertex, face multiplicity c8, 8
Petrie polygons
holes
2nd-order Petrie polygons
3rd-order holes
3rd-order Petrie polygons
4, each with 2 edges
2, each with 4 edges
4, each with 2 edges
1, with 8 edges
4, each with 2 edges
rotational symmetry groupC8, with 8 elements
full symmetry groupD16, with 16 elements
its presentation c< r, s, t | t2, r3s‑1, sr2s, (r‑1t)2 >
C&D number cR2.6
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 hemi-8-hosohedron.

It can be 2-fold covered to give S3:{8,8}4.
It can be 2-fold covered to give S3:{8,8}2.

It can be rectified to give S2:{8,4}.

It can be derived by stellation (with path <2,1;1,2>) from {4,4}(1,0). The density of the stellation is 6.

It is a member of series s.

List of regular maps in orientable genus 2.

Underlying Graph

Its skeleton is 4 . 1-cycle.

Other Regular Maps

General Index

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