Dice and the Minor Arcana: Opsopaus's geometrical approach

In his article "Tarot Divination Without Tarot Cards" (qv), John Opsopaus proposes a system of correspondences between the 56 cards of the Minor Arcana and the 56 possible rolls of three dice. This is analogous to his systems for mapping the 21 trumps to the 21 possible throws of two dice -- but is necessarily more complicated because the Minor Arcana are structured in a way that the trumps are not. While the trumps are numbered in a linear fashion, the Minor Arcana are grouped into four suits, each of which has 10 numbered (or "pip") cards and four face (or "court") cards.

Just as 21 is a triangular number, 56 is a tetrahedral one. Since 10 is also a tetrahedral number, the pips of each suit can be assigned to the smaller tetrahedron at one of the corners of the larger one. Once this is done, there remain 16 points at the center, arranged in the shape of a truncated tetrahedron, and these can be assigned to the courts.

The diagram below (which is my own work but is based closely on Opsopaus) shows how the 6th tetrahedral number can be divided into four smaller tetrahedra (red, yellow, green, blue) and a truncated tetrahedron (purple). Purple points represent court cards, and the other four colors represent the four suits of pips.

This is a great way of dealing with the pips, but the problem is that the courts are also divided into four suits, and there seems to be no natural way of quartering our central truncated tetrahedron.

One way of dealing with the courts is to associate each of the court ranks with one of the suits -- which has traditionally been done by way of mapping both the court ranks and the suits to the four classical elements. One popular system is Kings/Clubs/Fire, Queens/Cups/Water, Knights/Swords/Air, Knaves/Coins/Earth.

Notice that our truncated tetrahedron is made up of four hexagons, each of which faces one of the four pip-tetrahedra. For example, in the diagram above, the top surface of the truncated tetrahedron is a hexagon, comprising the rolls {334, 344, 335, 345, 355, 346, 356}, and facing the red tetrahedron. If we assign the red tetrahedron to the suit of Clubs, say, which is associated with the court rank of Kings, then the seven rolls on the red-facing hexagon will correspond to the seven court cards which are Clubs and/or Kings. The roll 345, which is in the center and which thus belongs exclusively to the red-facing hexagon, corresponds to the King of Clubs. Each of the remaining six rolls is shared with one of the other hexagons. For example, the rolls 355 and 356 belong to both the red-facing and the blue-facing hexagons. If we assign blue to Cups, corresponding to Queens, then one of these rolls will be the King of Cups, and the other will be the Queen of Clubs; we can perhaps assign the higher toll, 356, to the former on the grounds that a King should outrank a Queen.

These examples are just examples. I have not yet thought out which tetrahedron should correspond to which suit or any of the other details. Nevertheless, Opsopaus's basic schema seems to have a lot going for it.