Why do Fullerenes have even number of carbon atoms? My teacher started a chapter called &quot;Carbon and its compounds&quot;, Which is just an intro to organic chemistry . In which she taught about fullerenes structure and examples and also told that fullerenes have even number of carbon atoms. I got curious and asked why but she didn't answer me. So I went and googled it but still did not get any answer. Is there any exception or any reason behind it?
The structure of (closed) fullerenes is governed by Euler’s polyhedron formula: vertices (carbon atoms) + edges (bonds) - faces = 2. Geometric constraints determine that at least some of the faces must be pentagons or heptagons, and that the number of atoms must be even.