JavaScript: reverse mapping from an object id to that object

I have a class Rectangle which has a prop called id that indicates the uniqueness of that instance of Rectangle

class Rectangle {
  constructor(desc) {
    this.desc = desc
    this.id = Symbol()
  }
}

Later I need to put the id to some other data structure and I need a quick way to look up that Rectangle instance using the id

To achieve this I need to manually create a map e.g.

const r1 = new Rectangle('first')
const r2 = new Rectangle('second')
const r3 = new Rectangle('third')

const map = {
  [r1.id]: r1,
  [r2.id]: r2,
  [r3.id]: r3,
}

So I can do to get the reference of r1 if I need to

map[r1.id]

I wonder if there is a programmatic way to achieve this reverse mapping where id is the key and the Rectangle instance is the value?

Also, I would appreciate it if someone can suggest a better name for the map - right now the name map is not really descriptive.

Lastly, I wonder if we can get rid of id and just use the reference of the Rectangle instance? I know the answer is probably "it depends" but I think most of the time we would need an id for the instances or objects. I wonder if in what circumstances using only references is not going to cut it?

from JavaScript: reverse mapping from an object id to that object