S2:{3,8}

Statistics

genus c2, orientable
Schläfli formula c{3,8}
V / F / E c 6 / 16 / 24
notesreplete is not a polyhedral map permutes its vertices evenly
vertex, face multiplicity c2, 1
Petrie polygons
holes
2nd-order Petrie polygons
3rd-order holes
3rd-order Petrie polygons
4th-order holes
4, each with 12 edges
6, each with 8 edges
6, each with 8 edges
8, each with 6 edges
4, each with 12 edges
24, each with 2 edges
antipodal sets3 of ( 2v ), 4 of ( 4f ), 12 of ( 2e )
rotational symmetry groupGL(2,3), with 48 elements
full symmetry groupTucker's group, with 96 elements
its presentation c< r, s, t | t2, r‑3, (rs)2, (rt)2, (st)2, (rs‑3)2 >
C&D number cR2.1
The statistics marked c are from the published work of Professor Marston Conder.

Relations to other Regular Maps

Its dual is S2:{8,3}.

Its Petrie dual is N16.7′.

It can be 2-fold covered to give S3:{3,8}.

It can be 2-split to give R11.6.
It can be 5-split to give R38.5′.
It can be 7-split to give R56.10′.
It can be 10-split to give R83.7′.
It can be 11-split to give R92.11′.

It can be rectified to give rectification of S2:{8,3}.

It can be obtained by triambulating S4:{5,4}.

It can be stellated (with path <1,-1>) to give S2:{4,8}. The density of the stellation is 3.
It can be stellated (with path <>/2) to give S2:{8,4}. The density of the stellation is 2.

List of regular maps in orientable genus 2.

Underlying Graph

Its skeleton is 2 . K2,2,2.

Comments

This regular map features in Jarke J. van Wijk's movie Symmetric Tiling of Closed Surfaces: Visualization of Regular Maps, 1:10 seconds from the start. It is shown as a "wireframe diagram", on 3-fold K2. The wireframe is arranged as the skeleton of the 3-hosohedron.


Other Regular Maps

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The image on this page is copyright © 2010 N. Wedd