Seeded Dice Roller

After a desired face is chosen, a duplicate die is made. The physics of the initial velocity and torque values that will be used for the die roll are simulated on duplicate until it would become still. During each simulated step, the transform values of the duplicate are recorded for later use. Once the simulation is finished, if the duplicate die is not already showing the chosen face, it is rotated to show that face in the same orientation as the roll result. This rotation is the amount that the original die must also be rotated from its starting orientation in order to end up rolling the desired result.

Once all this is calculated, the recorded simulation steps, with the rotational offset, are applied to the original die one frame at a time. This gives the appearance that the die is being physically rolled to produce the predefined result.

The representation of the die is also written in such a way as to be agnostic of what each face represents; all the die knows is what face has been rolled, it's up to the handler consuming the result to decide what that result means. This makes it easy to create custom dice, allowing the user to map any data type of their choice to each face with whatever code is interpreting the roll result.

And of course, the mesh can look like whatever you want, as long as the collider used in the physics simulation and the layout of the faces follow the isomorphism rule.