
genus ^{c}  5, nonorientable 
Schläfli formula ^{c}  {10,4} 
V / F / E ^{c}  5 / 2 / 10 
notes  
vertex, face multiplicity ^{c}  1, 10 
5, each with 4 edges 2 double, each with 10 edges  
antipodal sets  5 of ( v, p1 ), 1 of ( 2f ), 1 of ( 2h ) 
rotational symmetry group  Frob(20), with 20 elements 
full symmetry group  Frob(20), with 20 elements 
Its Petrie dual is
It can be 2fold covered to give
List of regular maps in nonorientable genus 5.
Its skeleton is K_{5}.
We see that this is not a regular map if we arbitrarily label the vertices 0,1,2,3,4 and then follow the perimeter of a face. The vertices occur in the order 0410213243, so only five of the ten rotations of a face are symmetry operations.
Orientable  
Nonorientable 
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