Can cycloaddition reactions be antarafacial?

Cycloaddition reactions of the form [4+2] and [2+2] are always suprafacial, as the geometry is too constrained to allow for antarafacial interaction between the FMO's. However, **for cycloaddition of longer chains, say [6+6] cycloaddition, can the cycloaddition be antarafacial?**


Here's a small scheme I came up with for antarafacial cycloadditions, and the resulting product:


![Frontier orbitals for a hypothetical antarafacial [6+6] cycloaddition](https://i.stack.imgur.com/DNboR.png)
**Is this reaction possible?** I haven't been able to encounter any literature online for reactions of this type, which is why I'm doubtful. I just took [6+6] as an example, but if there are references of other conjugated systems undergoing antarafacial cycloaddition, they would be helpful.


