Toroidal and Klein bottle fullerenes

Spherical and toroidal fullerenes have an extensive chemical literature, and Klein bottle polyhexes have been considered, for example, in [Kir97, KlZh97]. 

Note that at least one spherical fullerene with v vertices exists for all even v with v 20, except for the case v = 22 ([GrMo63]). 

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