
genus ^{c}  4, orientable 
Schläfli formula ^{c}  {3,12} 
V / F / E ^{c}  6 / 24 / 36 
notes  
vertex, face multiplicity ^{c}  3, 1 
12 Hamiltonian, each with 6 edges 6, each with 12 edges 18, each with 4 edges 24, each with 3 edges 12 Hamiltonian, each with 6 edges 12 double, each with 6 edges 36, each with 2 edges 24, each with 3 edges 12 Hamiltonian, each with 6 edges 18, each with 4 edges  
rotational symmetry group  72 elements. 
full symmetry group  144 elements. 
its presentation ^{c}  < r, s, t  t^{2}, r^{‑3}, (rs)^{2}, (rt)^{2}, (st)^{2}, (sr^{‑1}s)^{3}, srs^{‑3}rs^{4} > 
C&D number ^{c}  R4.1 
The statistics marked ^{c} are from the published work of Professor Marston Conder. 
It can be 2split to give
It can be 4split to give
It can be 5split to give
It can be 7split to give
It can be obtained by triambulating
It can be stellated (with path <1,1>) to give
List of regular maps in orientable genus 4.
Its skeleton is 3 . K_{2,2,2}.
The 4thorder holes have six edges, but involve only three distinct edges and two distinct vertices.
Orientable  
Nonorientable 
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