


genus ^{c}  4, orientable 
Schläfli formula ^{c}  {6,12} 
V / F / E ^{c}  2 / 4 / 12 
notes  
vertex, face multiplicity ^{c}  12, 3 
6, each with 4 edges 4, each with 6 edges 12, each with 2 edges 8, each with 3 edges 6, each with 4 edges 4 double, each with 6 edges 12, each with 2 edges 4, each with 6 edges 6, each with 4 edges 12, each with 2 edges  
antipodal sets  1 of ( 2v ), 2 of ( 2f ), 6 of ( 2e ) 
rotational symmetry group  C3 ⋊ D8, with 24 elements 
full symmetry group  48 elements. 
its presentation ^{c}  < r, s, t  t^{2}, (rs)^{2}, (rt)^{2}, (st)^{2}, r^{6}, s^{‑1}r^{3}s^{‑1}r, s^{‑2}r^{2}s^{‑2} > 
C&D number ^{c}  R4.9 
The statistics marked ^{c} are from the published work of Professor Marston Conder. 
Its Petrie dual is
It can be truncated to give
It can be derived by stellation (with path <1,1>) from
It is a member of series p.
List of regular maps in orientable genus 4.
Its skeleton is 12 . K_{2}.
Orientable  
Nonorientable 
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