The dual Dyck map

Statistics

genus c3, orientable
Schläfli formula c{3,8}
V / F / E c 12 / 32 / 48
notesreplete singular is a polyhedral map permutes its vertices evenly
vertex, face multiplicity c1, 1
Petrie polygons
holes
2nd-order Petrie polygons
3rd-order holes
3rd-order Petrie polygons
4th-order holes
16, each with 6 edges
12, each with 8 edges
12, each with 8 edges
32, each with 3 edges
16, each with 6 edges
24, each with 4 edges
antipodal sets6 of ( 2v ), 16 of ( 2f ), 16 of ( 2e ), 16 of ( p, p3 )
rotational symmetry group96 elements.
full symmetry group192 elements.
its presentation c< r, s, t | t2, r‑3, (rs)2, (rt)2, (st)2, s8, (sr‑1s)3 >
C&D number cR3.2
The statistics marked c are from the published work of Professor Marston Conder.

Relations to other Regular Maps

Its dual is the Dyck map.

Its Petrie dual is N22.4.

It can be 2-fold covered to give S5:{3,8}.
It is a 2-fold cover of S2:{3,8}.

It can be 2-split to give R21.16.
It can be 5-split to give R75.7′.

It can be rectified to give the quasi-Dyck map.

It can be obtained by triambulating S3:{6,4}.

It can be stellated (with path <1,-1>) to give S3:{4,8|4} . The density of the stellation is 3.

List of regular maps in orientable genus 3.

Underlying Graph

Its skeleton is K4,4,4.

Comments

This regular map features in Jarke J. van Wijk's movie Symmetric Tiling of Closed Surfaces: Visualization of Regular Maps, 1:30 seconds from the start. It is shown as a "wireframe diagram", on K4. The wireframe is arranged as the skeleton of the tetrahedron.


Other Regular Maps

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