Find all elements of symmetry and the point group of fullerene C₇₀. Is C₇₀ 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  C2    01 2 3 4 5  C3    01 2 3 4 5  C4    01 2 3 4 5  C5    01 2 3 4 5  C6    01 2 3 4 5  C    01  i    01 2 3 4 5  S4    01 2 3 4 5  S6    01 2 3 4 5  S8    01 2 3 4 5   (vert.)    01 2 3 4 5   (hori.)

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

chirality:  chiral  achiral