A long time ago I read somewhere that when you write a scientific article you may use the word “very” very freely. Then at proof-reading you just have to go over everything a second time and scratch out every, really every, occurrence of that word from your article. Anyway, my talk will be about a class of knotted trivalent graphs which is obviously very 3D and nothing planar, yet it forms a planar algebra. Indeed, a very planar algebra - so planar that unlike, say, tangles, it cannot be generalized to higher genus ambient surfaces. The resulting planar algebra is quite useful - it provides a Reidemeister-move planar context for a universal finite type invariant. I’ll mention that and explain a bit, but my main reason for talking about this very non-planar very planar algebra is simply that it is amusing.