

genus ^{c}  4, nonorientable 
Schläfli formula ^{c}  {6,4} 
V / F / E ^{c}  6 / 4 / 12 
notes  
vertex, face multiplicity ^{c}  1, 2 
8, each with 3 edges 6, each with 4 edges  
antipodal sets  3 of ( 2v, h ), 4 of ( f, 2p ), 6 of ( 2e ) 
rotational symmetry group  S4×C2, with 48 elements 
full symmetry group  S4×C2, with 48 elements 
its presentation ^{c}  < r, s, t  t^{2}, s^{4}, (sr)^{2}, (st)^{2}, (rt)^{2}, (sr^{‑2})^{2}, r^{6}, sr^{‑1}s^{‑2}r^{‑2}t > 
C&D number ^{c}  N4.2′ 
The statistics marked ^{c} are from the published work of Professor Marston Conder. 
Its dual is
Its Petrie dual is
It can be 2fold covered to give
It can be rectified to give
It is the full shuriken of
List of regular maps in nonorientable genus 4.
Its skeleton is K_{2,2,2}.
Orientable  
Nonorientable 
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