

genus ^{c}  4, orientable 
Schläfli formula ^{c}  {12,6} 
V / F / E ^{c}  4 / 2 / 12 
notes  
vertex, face multiplicity ^{c}  3, 12 
6 Hamiltonian, each with 4 edges 4 double, each with 6 edges 12, each with 2 edges 6 Hamiltonian, each with 4 edges  
antipodal sets  2 of ( 2v ), 1 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}, (sr)^{2}, (st)^{2}, (rt)^{2}, s^{6}, r^{‑1}s^{3}r^{‑1}s, r^{‑2}s^{2}r^{‑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 5split to give
It can be 7split to give
It can be 11split to give
It is a member of series q.
List of regular maps in orientable genus 4.
Its skeleton is 3 . 4cycle.
Orientable  
Nonorientable 
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