The dual Dyck map

Statistics

genus c	3, orientable
Schläfli formula c	{3,8}
V / F / E c	12 / 32 / 48
notes
vertex, face multiplicity c	1, 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 sets	6 of ( 2v ), 16 of ( 2f ), 16 of ( 2e ), 16 of ( p, p3 )
rotational symmetry group	96 elements.
full symmetry group	192 elements.
its presentation c	< r, s, t | t2, r‑3, (rs)2, (rt)2, (st)2, s8, (sr‑1s)3 >
C&D number c	R3.2
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 The Fricke-Klein map.
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 is its own 3-hole derivative.

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 K_4,4,4.

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