Yes. Since one carbon is joined with only other 3 carbons and not 4 like diamond, so each Carbon atom must have one double bond. But two C atoms are joined by one double bond so we can conclude that no of double bonds should be half the no of C atoms in Fullerines.
We know fullerines have 60 Carbon atoms so no of double bonds in fullerines is = 30.
Above mentioned structure is exactly like American Soccerball which contains 12 pentagons and 20 hexagons.
Arranging 12 pentagons and 20 hexagons in a proper manner to form a closed sphere will lead to the above structure with 60 vertices each representing one C atom.
So the simplest way to arrange 60 C atoms in a sphere form is to form 12 pentagons and 20 hexagons and joining them to make a sphere.
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