


genus ^{c}  4, orientable 
Schläfli formula ^{c}  {6,6} 
V / F / E ^{c}  6 / 6 / 18 
notes  
vertex, face multiplicity ^{c}  2, 3 
6 Hamiltonian, each with 6 edges 6 Hamiltonian, each with 6 edges 6 Hamiltonian, each with 6 edges 18, each with 2 edges  
antipodal sets  3 of ( 2f ), 3 of ( 2e, 2h3 ) 
rotational symmetry group  36 elements. 
full symmetry group  72 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^{6} > 
C&D number ^{c}  R4.8 
The statistics marked ^{c} are from the published work of Professor Marston Conder. 
Its dual is
It is selfPetrie dual.
It can be derived by stellation (with path <1,1;1,1>) from
List of regular maps in orientable genus 4.
Its skeleton is 2 . K_{3,3}.
The second diagram above, with one hexagonal "hole" in its centre, was derived from the diagram of its dual on page 46 of ^{H01}, where it is considered as a dessin d'enfant. That graph is bipartite, and the actions of the dessin act on the edges of the graph to generate S3×C3. The authors obtained it by a method they term "origami".
Orientable  
Nonorientable 
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