
genus ^{c}  0, orientable 
Schläfli formula ^{c}  {3,5} 
V / F / E ^{c}  12 / 20 / 30 
notes  
vertex, face multiplicity ^{c}  1, 1 
6, each with 10 edges 12, each with 5 edges 10, each with 6 edges  
antipodal sets  6 of ( 2v, 2h2; p1 ), 10 of ( 2f; p2 ), 15 of ( 2e ) 
rotational symmetry group  A5, with 60 elements 
full symmetry group  A5×C2, with 120 elements 
its presentation ^{c}  < r, s, t  r^{2}, s^{2}, t^{2}, (rs)^{3}, (st)^{5}, (rt)^{2} > 
C&D number ^{c}  R0.3 
The statistics marked ^{c} are from the published work of Professor Marston Conder. 
Its dual is
Its Petrie dual is
It is a 2fold cover of
It can be 2split to give
It can be rectified to give
Its 2hole derivative is
Its full shuriken is
It can be stellated (with path <>/2) to give
It can be stellated (with path <1/1>) to give
It can be stellated (with path <1,1>/2) to give
It can be derived by stellation (with path <1,1>/2) from
List of regular maps in orientable genus 0.
Its skeleton is icosahedron.
This is one of the five "Platonic solids".
A4 
A5 
Orientable  
Nonorientable 
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