Neighbouring feature that share more than 2 vertices in Atlas

Question

Is there a way to filter polygons that share more than 2 vertices with a feature?
I have a problem where I have a layer being controlled by Atlas, and I would like to show on Atlas only the coverage feature and the neighbouring features that share more than 2 vertices with it.
Up until now I can achieve what is in the first image using touches($geometry, @atlas_geometry) in the filter in rule-based symbology. But I wanted something like in the second image. Is there a way to do that?

JGH · Accepted Answer

Using the ruled based symbology filter, you can compute the intersection and keep the ones having more than 1 point
num_points(intersection($geometry,@atlas_geometry))>1

Neighbouring feature that share more than 2 vertices in Atlas

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