
In addition to annual chronological cycle of the sun and geodetic lines of
terrestrial globe it is possible to correlate hexagrams of the Book of Changes iching
to traditional Chinese chronologic system or otherwise to tell classical cyclic
calendar which has duration of 60 years which are connected with 12 zodiacal
animals. Namely with the cyclic Chinese calendar in which twelve zodiacal
animals are interconnected with five substances, that in the sum is a basis of
60years chronological cycle, as 12x5=60.
Because sixty hexagrams within the logic system of binary symbols of the Chinese
Book of Changes form five spheres which correspond with five 12years
chronological periods. And four hexagrams with serial numbers 1, 2, 63, 64 form
a cross outside of chronological cycle, that is shown on the chart.
Cross of hexagrams iching symbolizes four geographic
directions or spatial coordinates, and also four world elements from the
view point of astrology and classical Greek philosophy. Ground  north  winter  1st hexagram consists of three digrams in which all lines are entire, that corresponds to number 9 of Chinese numerology. Air  south  summer  2nd hexagram consists of digrams in which all lines are break, that corresponds to number 6 of Chinese numerology. Water  west  autumn  63rd hexagram consists of digrams in which top lines are break and bottom are entire, that corresponds to number 8 of Chinese numerology. Fire  east  spring  64th hexagram consists of digrams in which top lines are entire and bottom are break, that corresponds to number 7 of Chinese numerology. 
Sixty hexagrams iching in five spheres symbolize five substances of Chinese
philosophy, that is shown on following charts.
Dark figures on charts specify serial numbers of hexagrams according to
sequence in the Book of Changes, and white figures in dark circles correspond to
numerical values. And also these charts show physiognomic symbols of human
facial emotions which correspond with hexagrams iching.
First sphere  substance of tree.

Second sphere  substance of fire.

Third sphere  substance of ground.

Fourth sphere  substance of metal.

Fifth sphere  substance of water.

The shown geometrical arrangements or spatial
configurations of hexagrams of the Book of Changes iching are named by
the term of "sphere" as they are schematic projections of
threedimensional space on a plane. 

Hexagrams of the Chinese Book of Changes iching in the shown five spheres
correspond with zodiac signs and astrological circle which symbolizes current of
time, or otherwise to tell celestial movement of heavenly bodies and sequence of
historical events.
Ratio of hexagrams with zodiac signs and astrological circle are certain by
physiognomic symbols of human facial emotions. Namely spheres are organized
according to ratios of physiognomic symbols with quarters or quadrants of
astrological circle.
Spring quarter of astrological circle  zodiac signs Aries,Taurus, Gemini
 joyful emotions of eyes.
Summer quarter of astrological circle  zodiac signs Crab, Leo, Virgo 
open emotional expressions of eyes.
Autumn quarter of astrological circle  zodiac signs Libra, Scorpio,
Sagittarius  sad expressions of eyes.
Winter quarter of astrological circle  zodiac signs Capricorn, Aquarius,
Pisces  quiet emotions of eyes.
Emotional expressions of eyebrows and mouth in the shown charts too are
organized according to rules of astrology, namely according with ratio of
zodiacal signs with triangles which correspond to four elements or have angular
sizes of 150x60x150 degrees.
For example, emotional expressions of eyebrows and mouth in the fifth sphere
correspond with zodiacal signs as shown in following two charts.
Left chart  emotional expressions of eyebrows.
Joyful eyebrows  red triangle  zodiacal signs of fire element: Aries, Leo, Sagittarius.
Quiet eyebrows  dark triangle  signs of zodiac in ground element: Taurus, Virgo, Capricorn.
Sad eyebrows  green triangle  zodiacal signs on element of air: Gemini, Libra, Aquarius.
Open eyebrows  blue triangle  zodiac signs of water element: Crab, Scorpio, Pisces.
Right scheme  emotional expressions of a mouth.
Sad mouth  red triangle  signs of zodiac Aries, Virgo, Scorpio.
Quiet mouth  blue triangle  signs of zodiac Crab, Sagittarius, Aquarius.
Joyful mouth  green triangle  signs of zodiac Libra, Pisces, Taurus.
Open mouth  dark triangle  signs of zodiac Capricorn, Gemini, Leo.
Physiognomic symbols of human emotions in different spheres correspond with
triangles of zodiacal signs differently.
It is impossible to formulate logical principle according to which hexagrams
iching and corresponding physiognomic symbols of facial emotions are
organized in spatial spheres and are compared to zodiacal signs. But this
logical principle can be seen on following charts where numerical values of
64 hexagrams in cells of a magic square are shown. Namely grey color
specifies positions of hexagrams of five spheres in cells of a magic square.
First and fifth spheres have mathematical sums of numerical values 316 and
464, that in aggregate forms number 316+464=780.
Second and fourth spheres have mathematical sums of numerical values 476 and
304, that too forms total number 476+304=780.
Third sphere has mathematical sum of numerical values 402. But if to add to the
third sphere numerical values of four hexagrams which form a cross outside of
chronological cycle of five spheres then total number is 402+1+25+50+42=520.
Numbers 520 and 780 correspond with mathematical sums of numerical values on
verticals and horizontals of magic square, as 520/2=260 and 780/3=260.
Number 260 corresponds to quantity of days in the chronological cycle of Tzolkin
in the ritual or sacral calendar of Mayan civilization.
Look information about 260 days of the chronological cycle Tzolkin in Mayan
calendar within other website www.wordgame.64g.ru
on the seventh page in section which is named as
letters of gods.
If other socalled associative magic square will be used then mathematical
sums of numerical values in five spheres will be ideal, that is shown on the
following chart.
Numbers symmetric concerning the center in the associative magic square
form identical sums. For example, 01+64=65 or 29+36=65, also mathematical sums
of numbers in all spheres have size 390 or otherwise to tell are ideal, that
differs from the previous usual magic square.
Also pay attention that opposite hexagrams and physiognomic symbols in five
spheres correspond to numbers which are symmetric concerning the center in the
associative magic square.
The shown associative magic square can be applied instead of usual in the
conjectural mantic game which is presented
on pages of this website, also for analyses of mathematical laws according to
which traditional sequence of 64 hexagrams of the Chinese canon iching is
organized. But it is necessary to consider that ratio of numbers of the usual
magic square with serial numbers of hexagrams iching allow to see mathematical
laws which are unobvious according to numbers of associative rectangular digital
matrix of magicians.
Or it is possible to tell that comparative analyses of logic ratios of diverse
magic squares with serial numbers of hexagrams iching allow to see mathematical
laws according to which structural sequence of the ancient Chinese Book of
Changes is organized.
Also serial numbers of 64 hexagrams of the Chinese Book of Changes iching form
mathematical laws according to which five spheres are organized. Namely if 64
hexagrams are located in cells of a magic square according to numerical values
then serial numbers form total numbers which are shown on following charts.
First sphere. Tree 444.

Second sphere. Fire 409.

Third sphere. Ground 314.

Fourth sphere. Metal 409.

Fifth sphere. Water 374.

Mathematical sums of serial numbers in the second and fourth spheres are 409.
Mathematical sums of serial numbers in the first and fifth spheres are 444 and
374. But in the first and fifth spheres there are especial numerical ratios.
444374=70/2=35.
44435=409.
374+35=409.
Mathematical sum of serial numbers in the third sphere is 314. But if third
sphere has addition of serial numbers of four hexagrams which form a cross then
total sum is equal to the cipher of first sphere, as 1+2+63+64=130+314=444.
These numerical ratios allow to speak that the shown spatial spheres correspond
to mathematical laws according to which sequential order of 64 hexagrams of the
Chinese Book of Changes iching is constructed. And also these numerical ratios
allow to speak that consecutive order of hexagrams iching in the Chinese Book
of Changes is not casual.
Because symbols of iching in five spheres are organized according to quarters
of astrological circle. And also according with triangles which correspond to
four elements or have angular sizes of 150x60x150 degrees within astrological
circle, and as a result numerical values of hexagrams form regular ciphers or
natural figures which correspond with mathematical sums of numbers on verticals
and horizontals of magic square. And also serial numbers of hexagrams iching in
five spheres form regular ciphers or natural numerical ratios as a result of
coordination with astrological circle and magic square.
I cannot explain the law or logic principle according to which consecutive order
of hexagrams iching in the Chinese Book of Changes is constructed. I only pay
your attention that the sequence is not casual.
It is a question of sequence which has been established by legendary King Wen,
or which has been received by the Chinese civilization from other unknown
sources.
Following page shows parities of hexagrams of the Book of Changes iching in five spheres with zodiacal circle of twelve animals which form chronological cycle of traditional Chinese calendar and astrology.

On other pages in this section of website it is possible to find information about natural phenomena and atmospheric processes, geodetic lines of the Earth and primordial deities of Egyptian cosmology, chronology of New Age and celestial birth map of French artist, constellations and stars of heavenly sphere, precious gem stones and minerals, divination charts of Lian Shan and Gui Cang.