Three Impossible Dice

This is a project specifically made for the #FakeTTRPGJam. Please don't try and make these dice. You might fold the universe in on itself.

The Diadem Apparatus allows the user to peer into parallel universes, alternate realities and adjacent dimensions. In one such attempt, I glimpsed a world that left me with the impression of  a chord with a note out of tune. There, I saw people much like us, play a game called Futility, which looked like our tabletop role-playing games. They were on edition i and these were the dice they used:

1d0:

Midenahedron, the zero-sided die.

Rolling this die produces no result.

1d1:

Henahedron, the one-sided die.

Rolling this die always produces the same result.

1d∞:

Apeirohedron, the infinite-sided die.

Rolling this die produces any result.

All the dice described above seemed pointless in function. They narrowed down nothing. Connected to no meaningful probabilities or tables or provided any kind of resolution. And yet, I have the nagging feeling that they held immense meaning to the players of this game.