
Except for linear sequence of hexagrams ijing in the Book of Changes there
are arrangements of hexagrams in a square, and also circular and some other
spatial arrangements which are known from ancient books. For example, circular
and square arrangements which have been established by emperor Fu Hsi (Paohsi)
are known. But also in texts of ancient books there is an information about
conjectural or otherwise to tell mantic systems which have been lost, namely in
the past there were arrangements which were applied as conjectural and calendar
systems, but it is not known about these systems now. In particular in texts of
ancient books there is an information on systems LinShan and KueiChuang which are lost.
These lost mantic systems can be reconstructed.
Namely in comments of the Book of Changes in The Great Appendix there are
descriptions of 13 hexagrams which are actually equivalent to 13 hexagonal
symbols which are shown in figure:

The detailed information about shown 13 hexagonal symbols and comments of The Great Appendix look on pages of this website in section which has the name astropsychophysiology. 

These hexagonal symbols allow to create five groups on 12 hexagrams ijing in each, namely it is possible to group according to quantity of the entire and break lines in 13 hexagonal symbols, and according to quantity of the entire and break lines in 64 hexagrams.
The first group.
07 08 15 16 23 2409 10 13 14 43 44
Hexagrams of the first group have one entire and five break lines, or have one break and five entire lines that corresponds to two hexagonal symbols.
The second group.
17 18 21 22 47 48 53 54 55 56 59 60
Hexagrams of the second group have three entire and three break lines that corresponds to one hexagonal symbol.
The third group.
03 04 35 36 39 40
05 06 37 38 49 50
Hexagrams of the third group have two entire and four break lines, or have four entire and two break lines that corresponds to two hexagonal symbols.
The fourth group.
19 20 45 46 27 62
25 26 33 34 28 61
Hexagrams of the fourth group have two entire and four break lines, or have four entire and two break lines that corresponds to two hexagonal symbols.
The fifth group.
29 51 52
30 57 58
11 12 31 32 41 42
Hexagrams of the fifth group have two entire and four break lines, or have four
entire and two break lines that corresponds to two hexagonal symbols. And also
hexagrams of the fifth group have three entire and three break lines that
corresponds to one hexagonal symbol.
In total there are five groups and 12 hexagrams ijing in each group that forms
set 12x5=60, and four hexagrams are outside of five groups.
01 02 63 64
Total 13 hexagonal symbols are equivalents of 64 hexagrams ijing.
Five groups and 12 hexagrams in each group are comparable to symbols of the
traditional Chinese calendar or the Chinese zodiac in which there are 12
animals: rat, bull, tiger, rabbit, dragon, snake, horse, goat, monkey, hen, dog,
pig; and 5 colors: blue, red, yellow, white, black.
And also 12 hexagrams ijing in five groups are comparable with hexadecimal (sexagesimal)
scale of notation which was known in ancient Babylon and is a basis for
measurement of time as one hour of time consists of 60 minutes. Or are
comparable to numbers of the Chinese numerology in which there are three groups
on five numbers as 3x5=15x4=60, that corresponds to 60 hexagrams ijing in five
groups.
These comparisons allow to assume about ancient mantic and calendar systems
which could be connected with hexagrams ijing.
The information on the traditional Chinese
zodiac and numbers of the Chinese
numerology look in other sections of this website.
The following page shows circular schemes or otherwise to tell circular spatial arrangements of hexagrams ijing in five groups.
