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Different families of fullerenes taking as a basis their progenitors, mini-fullerenes,
and graph theory were constructed. They are: a family of a bi-trefoil:
C14, C18, C24, C30, C36;
a family of truncated bipyramids:
C14, C18, C24 C30, C36;
a family of cupola half-fullerenes:
C10, C12, C16, C20, C24;
and a family of 4-6-equator fullerenes:
C20, C24, C32, C40, C48. All the
families contain five members and have a layer structure. By analogy with geography, we can
distinguish two frigid zones composed of pentagons and a torrid zone composed of hexagons.
The smallest fullerenes of each family are exceptions; its frigid zones are formed of squares.
Another interesting feature is that the torrid zone in the family of 4-6-equator fullerenes:
C20,
C24, C32, C40, and C48
is composed of square-hexagon pairs. We have also constructed
a family of cupola half-fullerenes:
C10, C12, C16, C20, and C24 with the help of transition to
modified graphs introduced in [3], where a cluster of three or four atoms being considered as
a big point (vertex) contrary to a zero-size point (vertex) of a common graph.
Keywords: mini-fullerenes; families of fullerenes; graph theory |
full paper (pdf, 1568 Kb)