Face object top to camera or Keep current top with LookAt

Hey there all. So here's my question,

What I want to do is rotate an object so that it's current top face turns to camera. Any idea how I can do this? Something related to Vector3.up or maybe storing initial rotation to create a custom rotation match comes to mind but I cannot exactly put my finger on it.

To make it easier to understand, let's take a dice for example. And let's say it drops to floor with random rotation with rigidbody. I'd like that top number to face the camera.