
genus ^{c}  12, nonorientable 
Schläfli formula ^{c}  {6,4} 
V / F / E ^{c}  30 / 20 / 60 
notes  
vertex, face multiplicity ^{c}  1, 1 
24, each with 5 edges 20, each with 6 edges  
antipodal sets  15 of ( 2v ), 10 of ( 2f, 2h ), 30 of ( 2e ), 12 of ( 2p ) 
rotational symmetry group  240 elements. 
full symmetry group  240 elements. 
its presentation ^{c}  < r, s, t  t^{2}, s^{4}, (sr)^{2}, (st)^{2}, (rt)^{2}, r^{6}, s^{‑1}rsr^{‑1}s^{‑2}r^{‑1}sr^{2}t > 
C&D number ^{c}  N12.1′ 
The statistics marked ^{c} are from the published work of Professor Marston Conder. 
Its dual is
Its Petrie dual is
It is the full shuriken of
List of regular maps in nonorientable genus 12.
Orientable  
Nonorientable 
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