Dice are an object type in Tabletop Playground. When you pick up and throw dice, they get a random spin and every player gets a notification with what was rolled once thrown dice come to rest. When you drop dice without throwing them, they behave as generic objects. Rotating a picked up die cycles through each face pointing up. You can also roll dice without picking them up by pressing the object action button.
Dice also have special tooltips: when hovering a single die, the tooltip will show which face is up. When multiple dice are selected, the tooltip shows how often each face is up and the sum of all faces. For custom dice, faces can also have names instead of numbers. The names are included in the tooltip, but not counted towards the sum.
If you want to create custom dice using the default models and your own textures, here are sample images that show where the faces of the dice are mapped to the texture: Dice UVs.