[jeffwass]

In this case, since all atoms form a ring, everything is symmetric within the plane so forces cancel out. So maybe it’s more stable than one would think, similar to cubane.

But upon further consideration , the potential energy surface may be more like a saddle point, with each atom having a stable local minimum in-plane but unstable local maxima perpendicular to the plane. (I’m not a chemist).

[gus_massa]

The atoms must be in a minimum of energy. They always oscillate a little due to thermodynamic and quantum effects. If they are in a saddle point the molecule blends until the atoms reach a minimum, until the atoms rearrange themselves in a different molecule or until the molecule split. (Or until they react with another molecule ...)

I studied a little of Chemistry, but this is out of the scope that I know well. IIUC correctly from https://en.wikipedia.org/wiki/Cubane the stability of cubane is not due to symmetry. The stability comes from the fact that locally it looks like a alkane, i.e. a molecule with Carbon and Hydrogen that only have single bonds. They are quite stable, the most common example is gasoline that is mostly alkanes.

Double bonds are more reactive. For example vegetable oils (that have also Oxygen, not only Carbon and Hydrogen) may have or not have double bonds. The one with many double bonds become rancid easier. https://en.wikipedia.org/wiki/Rancidification