Number of different colourings of fullerenes Some numerical examples using SYMMETRICA Generators of the symmetry groups of fullerenes Cycle indices of the symmetry groups of fullerenes

Cycle indices of the symmetry groups of fullerenes

Now we can compute the cycle indices of the symmetry groups of some fullerenes.
Please determine which group is acting? Where does this group act on? Which fullerene Cv to investigate. (Please enter only even v such that 24≤ v≤ 60, or v=20,70,80.) For v=40 or v=44 you further have to specify whether to use the D or T symmetry.

Furthermore please determine which representation - the standard or the alternating representation - of the group you are interested in. The cycle index of the alternating representation is computed as Z(R(Cv))-Z(S(Cv)) for achiral fullerenes Cv. These are those fullerenes which have not only rotational symmetries. For chiral fullerenes the alternating representation equals the standard representation.

v=
For starting computation, press the button .
harald.fripertinger "at" uni-graz.at, May 10, 2016

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