- * Apex of Greater Tetrahedron:
- The Initial Monad (1) is at the apex for the Intermediate
Elements (Air & Water = Swords & Cups). The Final
Monad (10) is at the apex for the Extreme Elements (Fire &
Earth = Wands and Pentacles).
- # Apex of Lesser Tetrahedron:
- The element corresponding to the suit and rank is at the apex (King/Wands = Fire, Knight/Swords = Air, Queen/Cups = Water, Page/Pentacles = Earth).

When the throws corresponding to two cards differ in just one
die (e.g. 124 and 134), we say there is a *path* between
those two cards. These paths are very important for understanding
the structure of the Minor Arcana. For example, there is an
ascending or descending path through the court cards of each suit
(e.g. 124 - 134 - 135 - 235 in Wands). Similarly, if you diagram
the paths among the pip cards of a suit you will learn much about
the structure of the Pythagorean Decad. For example, paths connect
the three Unities (Initial = 1, Hidden = 7, Final = 10). Also, do
not neglect path *between* the suits, which show many
interesting connections.

The pip cards are organized into three connected triangles of size 6, 3 and 1, which are the primary structure of the Decad:

The first triangle is 1; 2, 3; 4, 5, 6. It begins with the Initial Unity (1) and comprises both the First Triad (1, 2, 3) culminating in the First Perfection (3), and the Second Triad (4, 5, 6) culminating in the Second Perfection (6). The second triangle corresponds to the Third Triad (7, 8, 9) beginning with the Hidden Unity (7) and culminating in the Third Perfection (9). The third triangle corresponds to the Final Unity and Perfection (10). The Triad structure is shown in the chart above. (See the commentary on the Minor Arcana for these terms and for the structure of the Decad.)

The structure of the Minor Arcana is also revealed through the sums of the dice throws (e.g., a throw of 124 sums to 7). For example, the apices of the Greater Tetrahedron are assigned to the suits on the basis of the increasing density of their elements (111 = 3 = Fire = Wands, 116 = 8 = Air = Swords, 166 = 13 = Water = Cups, 666 = 18 = Earth = Pentacles). Also, in the court cards, the sums increase from Page through King, representing their potency. Further, the sums are increasing in each triangle in the pips of the Wands and Swords (which correspond to active, light, ascending elements), and decreasing in the Cups and Pentacles (passive, heavy, descending elements).

Observe also the ranges of the sums for the pips of each suit increase with density: Wands: 3 - 9, Swords: 6 - 12, Cups: 9 - 15, Pentacles: 12 - 18. For the light elements (Fire, Air), the 10 has the smallest sum; for the heavy elements (Water, Earth), the 10 has the greatest sum. The ranges for courts also increase with density: Wands: 7 - 10, Swords: 8 - 11, Cups: 10 - 13, Pentacles: 11 - 14.

It is also possible to convert from a dice throw to the corresponding astragali throw. Roll the three dice and write down the numbers in increasing order (as they are shown in the dice chart). Suppose the three numbers are XYZ. The corresponding astragali have X-1 1s, Y-X 3s, Z-Y 4s and 6-Z 6s. For example, the roll 226 has 2-1 1s, 2-2 3s, 6-2 4s and 6-6 6s, so it is 14444.

The remarks made about paths between dice throws also applies to astragali throws, as do the remarks about the structure of the Minor Arcana (the Triads etc.). (The astragali throws are not, however, naturally arranged in a tetrahedron.)

- Casting Dice or Astragali
- Casting Pebbles
- Drawing Contrasting Tokens
- Drawing Marked Tiles
- Casting Dodecahedra

To use astragali to choose a Major Arcanum, roll three astragali or one astragalus three times. Record the numerical values of the sides in increasing order (e.g. 334) and look up the corresponding trump (17.Moon). To choose a Minor Arcanum, roll five astragali (or one astragalus five times) and look at the chart in this chapter. Recall, however, that the astragali can produce only 20 trumps; 21.World is not possible. This problem is solved, again, by duplicate occurrences. If the first duplicate sums to an even number it is 0.Fool, if it sums to an odd, it's 21.World. A second duplicate occurrence is interpreted as the opposite of the first, regardless of whether it is even or odd (so if the first was Fool, the second is World, and vice versa). Any duplicates after the second require a reroll.

One can also get the effect of rolling five astragali to
choose a Minor Arcanum by using five black balls and three white
balls. Select them in order from a jar or bag. The number of 1s
is the number of blacks selected before the first white. The
number of 3s is the number of blacks between the first and
second whites. The number of 4s is the number of blacks between
the second and third whites. The number of 6s is the number of
blacks after the third white. It will be seen that this is
exactly the same procedure for using balls to get three dice
rolls, so the sequence of drawn balls determines both a roll of
three dice and a roll of five astragali. For choosing a Major
Arcanum, use the three white balls, but only *three*
black balls. Interpret as above.

For selecting a Major Arcanum according to the astragali, use six tiles marked 1346AZ. Draw three tiles. As for the dice, A means to duplicate the least number drawn and Z means to duplicate the greatest number drawn. So 36A is 336 and 4AZ is 444. For choosing a Minor, use a set of eight tiles marked 1, 3, 4, 6, A, B, C, D (or some similar series of four, such as I, II, III, IIII; or use cards from a deck of ordinary playing cards). Draw five tiles and arrange them according to the order 1346ABCD. So, we might have drawn 14ABD. Then, in order, replace A by the first number in the series, B by the second, C by the third and D by the fourth. In this case, in 14ABD we replace A by 1 to get 141BD, B by 4 to get 1414D, and D by 4 (in the fourth position) to get 14144. Therefore the throw is 11444.

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Last updated: Jan 6, 2018