Find all elements of symmetry and the point group of the famous soccer-like molecule C₆₀ (buckminsterfullerene). Is C₆₀ chiral or achiral?

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As usual with fullerenes, we left out the delocalized double bonds.

symmetry elements:    01 2 3 4 5 6 many  C2    01 2 3 4 5 6 many  C3    01 2 3 4 5 6 many  C4    01 2 3 4 5 6 many  C5    01 2 3 4 5 6 many  C6    01 2 3 4 5 6 many  C    01 2 3 4 5 6 many      01  i    01 2 3 4 5 6 many  S4    01 2 3 4 5 6 many  S6    01 2 3 4 5 6 many  S8

point group:  C2  C2v  C5  C5h  C6  C6h  Cs  Ci  D2  D2d  D2h  D5  D5d  D5h  D6  D6h  other

chirality:  chiral  achiral