# 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 polygonsholes2nd-order Petrie polygons3rd-order holes3rd-order Petrie polygons4th-order holes 16, each with 6 edges12, each with 8 edges12, each with 8 edges32, each with 3 edges16, each with 6 edges24, 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 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.

### 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

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