Labeling cube vertices with trigrams and Cartesian coordinates

The vertices have first been labeled with a letter (t=top; b=bottom) and a number (1, 2, 3, or 4) for easy identification and reference.

Next the eight trigrams are positioned, one at each of the eight vertices as follows:

b1  ☷  EARTH                    t1  ☵  WATER

b2  ☶  MOUNTAIN             t2  ☴   WIND

b3  ☲  FIRE                       t3  ☰   HEAVEN   

b4  ☳  THUNDER                t4  ☱   LAKE

Now let the side of the cube equal two units.

Let the center of the cube be located at Cartesian coordinate (0,0,0).

Let yang = +1 and yin = -1.

Let the first (bottom) line of a trigram represent the x dimension (left/right), directed from right (-) to left (+).* Let the second (middle) line of a trigram represent the y dimension (up/down), directed from bottom (-) to top (+). Let the third (top) line of a trigram represent the z dimension (forward/backward), directed from closer to the viewer (-) to farther from the viewer (+).**

Then the Cartesian coordinates will be as follows:

b1  ☷  (-1,-1,-1)   EARTH          t1  ☵  (-1,+1,-1)  WATER

b2  ☶  (-1,-1,+1)  MOUNTAIN   t2  ☴  (-1,+1,+1)  WIND

b3  ☲  (+1,-1,+1) FIRE             t3  ☰  (+1,+1,+1) HEAVEN 

b4  ☳  (+1,-1,-1)  THUNDER      t4  ☱ (+1,+1,-1)   LAKE

*This is opposite the Western convention but will make no difference as will be shown in the post to follow.

**The y and z dimensions have been interchanged here relative to the Western convention. These changes preserve certain prepotent associations between the trigrams and their compass points in the I Ching. In any diagram or display, the orientation of the three axes, as a whole, is arbitrary. However, the orientation of the axes relative to each other should always comply with the right-hand rule, unless specifically stated otherwise. All laws of physics and math assume this right-handedness, which ensures consistency. The orientation described here does in fact comply with the right-hand rule.

© 2012 Martin Hauser