
genus ^{c}  1, nonorientable 
Schläfli formula ^{c}  {3,5} 
V / F / E ^{c}  6 / 10 / 15 
notes  
vertex, face multiplicity ^{c}  1, 1 
6, each with 5 edges 6, each with 5 edges 10, each with 3 edges  
antipodal sets  6 of ( v, p1, h2 ), 10 of ( f, p2 ), 5 of ( 3e ) 
rotational symmetry group  A5, with 60 elements 
full symmetry group  A5, with 60 elements 
its presentation ^{c}  < r, s, t  r^{2}, s^{2}, t^{2}, (rs)^{3}, (st)^{5}, (rt)^{2}, (rsrsrt)^{2} > 
C&D number ^{c}  N1.2 
The statistics marked ^{c} are from the published work of Professor Marston Conder. 
Its dual is
Its Petrie dual is
It can be 2fold covered to give
It can be 2split to give
It can be rectified to give
Its full shuriken is
List of regular maps in nonorientable genus 1.
Its skeleton is K_{6}.
If you take a hemiicosahedron and glue another one to each face, and bend them round so that three meet at each edge, you will find that the 11 of them form a regular polytope, the 11cell, Schläfli symbol {3,5,3}. Its rotational symmetry group is PSL(2,11). Do not try this at home – it is not possible while you are embedded in 3space.
Orientable  
Nonorientable 
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