How to rotate a plane around a set of 3D points forever?

I am trying to reproduce a recreational math puzzle that was moddled in 2D on the youtube channel 3 Blue 1 Brown. The link can be found here.

I want to test if this workss in 3 dimensions using a plane instead of a line. So what i need to figure out to get started is how to have say 3 points in 3D space and a plane which starts centered on one of the points. So far I have this working. I was able to reproduce the 2D example in 3D space (all points have y pos = 1) using the following code:

 // Start is called before the first frame update
     void Start()
     {
         GameObject startingSphere = GameObject.Find("Sphere004");
         this.transform.position = startingSphere.transform.position;
         this.transform.Rotate(startingSphere.transform.position, 90);
 
     }
 
     // Update is called once per frame
     void Update()
     {
         this.transform.Rotate(0, .75f, 0);
     }
 
     private void OnTriggerEnter(Collider col)
     {
         this.transform.position = col.gameObject.transform.position;
     }

The plane has its rotation updated every frame and bounces around between the points exactly as it should. Because I am using triggers for the collisions the physics engine is not being applied at all.

Now I want to move the points so they are not all on y = 1 and have the plane rotate on all 3 axis. What I am first wondering is if I should not be using triggers and somehow just give the plane an arbitrary initial rotation and somehow have it keep going without slowing down. OR If i should be using triggers still and somehow calculating the normal of the plane and the point it is colliding with and then after updating the location of the plane to be centered on the new point, also updating its rotation to the new values, but i dont know how i would determine this.

I think the second answer is the right one, but im barely a beginner with Unity and my linear algebra is a bit rusty also.

Any help would be greatly appreciated!

Thanks!