"Arrangements and Relations"

(Wen pairs presented on a square grid)

Wen's pairs are well-ordered, but they lack a well-defined spatial arrangement


4 homogenous pairs of hexagrams (formed from identical trigrams) related through the complementarity relation


28 pairs of heterogenous hexagrams (formed from dissimilar trigrams) related through the figurative inversion relation


Xiantian arrangements are spatially defined with a clear pairing/ordering syntax

xiantian magic square

traditional xiantian arrangement

4 homogenous pairs of hexagrams form a diameter


28 hexagrams gird either side of this diameter

internal view of 4 x 4 x 4 hypercube

The hypercubic hexagram arrangement is well-defined but lacks ordering or pairing syntax entirely.


4 pairs of hexagrams comprise a cubic "core"


28 pairs of hexagrams form a "hull" around the core

unit cube 

Here, we use the unit cube to order the tesseract (hypercube).  Each of the unit cube's eight vertices (representing the trigrams) has seven outbound paths to each of the other vertices, totaling 56 paths.  Half of these paths are duplicates, in the sense that the paths connect the same pair of vertices.  Thus, the 56 paths comprise 28 pairs of heterogenous* hexagrams.  An outbound path and its reversal constitute a Wen Pair.
Each vertex can also loop back to itself.  These 8 loops constitute 4 pairs of homogenous* hexagrams.  Loops at antipodal corners (e.g. (0,1,1) and (1,0,0) ) also designate Wen pairs.