
genus ^{c}  0, orientable 
Schläfli formula ^{c}  {4,3} 
V / F / E ^{c}  8 / 6 / 12 
notes  
vertex, face multiplicity ^{c}  1, 1 
4, each with 6 edges  
antipodal sets  4 of ( 2v; p1 ), 3 of ( 2f ), 6 of ( 2e ) 
rotational symmetry group  S4, with 24 elements 
full symmetry group  S4×C2, with 48 elements 
its presentation ^{c}  < r, s, t  r^{2}, s^{2}, t^{2}, (rs)^{4}, (st)^{3}, (rt)^{2} > 
C&D number ^{c}  R0.2′ 
The statistics marked ^{c} are from the published work of Professor Marston Conder. 
Its dual is
Its Petrie dual is
It is a 2fold cover of
It can be rectified to give
It can be Eppstein tunnelled to give
It can be obtained by truncating
It can be pyritified (type 4/3/5/3) to give
It is the result of pyritifying (type 2/3/4/3)
Its half shuriken is
It can be stellated (with path <1>) to give the stella octangula. The density of the stellation is 2 * 1 = 2.
List of regular maps in orientable genus 0.
Its skeleton is cubic graph.
This is one of the five "Platonic solids".
This regular map features in Jarke J. van Wijk's movie Symmetric Tiling of Closed Surfaces: Visualization of Regular Maps, 0:10 seconds from the start. It is shown as a "wireframe diagram", on K_{1}. The wireframe is arranged as the skeleton of
C4×C2 
D8 
D8 
C2×C2×C2 
S4 
A4×C2 
S4×C2 
Orientable  
Nonorientable 
The images on this page are copyright © 2010 N. Wedd