The Dyck Map, S3:{8,3}

Statistics

genus c3, orientable
Schläfli formula c{8,3}
V / F / E c 32 / 12 / 48
notesreplete singular is a polyhedral map permutes its vertices evenly
vertex, face multiplicity c1, 1
Petrie polygons
16, each with 6 edges
antipodal sets16 of ( 2v ), 6 of ( 2f ), 16 of ( 2e )
rotational symmetry group96 elements.
full symmetry group192 elements.
its presentation c< r, s, t | t2, s‑3, (sr)2, (st)2, (rt)2, r8, (rs‑1r)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 S3:{3,8}.

Its Petrie dual is {6,3}(4,4).

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

It can be rectified to give the quasi-Dyck Map, S3:{8,3}.

It can be Eppstein tunnelled to give R19.2′.

It can be obtained by truncating S3:{4,8|4}.

List of regular maps in orientable genus 3.

Underlying Graph

Its skeleton is Dyck graph.

Comments

This regular map has been used as the design for a quilt, sewn from material cut from twelve shirts.

This regular map features in Jarke J. van Wijk's movie Symmetric Tiling of Closed Surfaces: Visualization of Regular Maps, 0:20 seconds from the start. It is shown as a "wireframe diagram", on K4. The wireframe is arranged as the skeleton of the tetrahedron.


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