# Precise definition of cylindrically symmetry in MO theory?

I was watching an MIT OpenCourseWare lecture on MO theory which mentioned that $$\sigma$$ orbitals are "cylindrically symmetrical." I was a bit confused, because I was under the assumption that the cross section of a $$\sigma$$ orbital is an ellipse, such that a $$\sigma$$ orbital is an ellipse that has undergone a full revolution around an axis. This is somewhat of a topology/nomenclature question, but seeing as the context is Chemistry, I though I'd post here first. Could anyone clear up the definition of cylindrical symmetry?

• You're right. A $\sigma$ bond would be more like an ellipsoid than a spherocylinder (capsule) and even less like a cylinder. All three of these would have a rotational axis. – MaxW Apr 17 at 0:25
• They just mean that, like a cylinder, there is an axis of infinite rotational symmetry $C_\infty$ – Andrew Apr 17 at 11:11