Converting the 3 nearest points of an object to a plane

So, I have this little planet (created using a subdivided mesh tool). I want to make that whenever the player is standing on a certain vertices, a plane is created between the 3 points of the part of the mesh that they're standing on. I honestly have no idea how I'd go about doing this, I'd appreciate any help if anybody could provide steps as to how I'd go about doing this or anything?