The Taiji and
the Twelve Sovereign hexagrams.

The Twelve Sovereign hexagrams are twelve hexagrams which show the ascend and descend of yang (represented by a straight line) and yin (represented by a broken line) energy. They represent the essence of the I Ching hexagrams.

As for the dusk and dawn of a year, on the winter solstice, in the eleventh lunar month, one yang arises; each thirty days adds another yang line: so one yang arising in the eleventh month makes Return , the second yang arising in the twelfth month makes Overseeing , the third yang arising in the first month makes Tranquility , the fourth yang arising in the second month makes Great Power , the fifth yang, arising in the third month makes Parting , and the sixth yang arising in the fourth month makes Heaven . These are the six yang hexagrams. In the fifth month, one yin arises, making Meeting , and the thirty days of each month add one yin line; in the sixth month the second yin arises, making Withdrawal , in the seventh month the third yin arises, making Obstruction , in the eighth month the fourth yin arises, making Observing , in the ninth month the fifth yin arises, making Stripping Away , and in the tenth month the sixth yin arises, making Earth . These are the six yin hexagrams. The six yang months are the dawn, the six yin months are the dusk; this is the dusk and dawn of a year. -- Liu Yiming, Commentary on Understanding Reality

These twelve hexagrams are linked to the twelve months of the year to create The Firing Times of the Greater Cycle the Sky ― The Sun.

The Cycle of the Sun -- Wei Boyang (Canton Qi - Triplex Unity)

At the new moon`s light lies Return
The Yang breath begins to spread through,
Going out and coming in without error.

At Overseeing , the furnace issues strips of light,
Opening the way for proper radiance.
Radiance and shine gradually advance.

Looking upward, it forms Tranquility .
The firm and the yielding both come to hold sway.
As Yin and Yang conjoin,
The small departs, the great approaches.

Gradually comes the turn of Great Strength .
Boldly standing at the gate to dawn.

At Parting the time has come for Yin to move into retreat,
For Yang has risen and has come to the force.

Heaven is strong, flourishing, and bright,
And lays itself over the four neighbourhoods.

At Meeting a new epoch comes to pass:
for the first time there is hoarfrost underfoot.

At Withdrawal it leaves its wordly place,  
gathering it's essence to store it up.   

At Obstruction there are stagnation and blockade,
and no new buds are generated.
Yin stretches and Yang bends.

Observation , with its equity and its balance,
examines the temper of autumn`s middle month.

Stripping Away tears its limbs and trunk,
Extinguishing its form.
The vital Breath is drained,
The Supreme spirit is forgotten and is lost.

The course comes to an end and turns around,
Returning to its origin in Earth .
Ever complying with the patterns of the Earth,
She receives heaven in herself, allowing it to unfold.

This cycle is also called The Celestial Mechanism.

The shallow may take the I Ching to be a book of divination, but the profound consider it the secret of the celestial mechanism.
-- Lu Dongbin (9th c. Taoist master, one of the eight immortals)
But this celestial mechanism of practicing reversal in the midst of accord has a secret which is communicated verbally and instructs the heart; one must seek the guidance of the true teacher, for it cannot be known through arbitrary guesswork. -- Liu Yiming, Inner teachings of Taoism.

When these twelve hexagrams are arranged in a circle, the following image on the left appears. The white represents yang and the gray represents yin. Hexagram #24 Return is positioned at #1, followed by hexagram #19 Overseeing at #2 and Hexagram #11 Tranquility at #3, etc. The first six hexagrams positioned at #1 to #6 show the increase of yang energy.

Increase means augmenting insufficient celestial energy; to augment what is insufficient means adding from one yang until there are six yangs, so that finally positive celestial yang is pure and complete.
-- Liu Yiming, The Taoist I Ching, hexagram #44 Meeting

When the area where yin and yang meet are traced, a spiral shape forms, which creates the same shape as Yin-Yang or Taiji symbol. From #7 to #12 yin energy increases.

When yang culminates, yin is inevitable; one yin surreptitiously arises, and the yang energy is damaged. ---- Liu Yiming, The Taoist I Ching, hexagram #44 Meeting

The Twelve Sovereign hexagrams are made up of six trigrams. The two remaining trigrams Fire ☲ (yin within yang or black within white) and Water ☵ (yang within yin or white within black) are placed inside the shape and the Taiji symbol is complete. This is the origin of the Taiji symbol.

Wei Boyang ends the verse on The Cycle of the Sun thus:

There is a dark (hidden) secret, remote and slight, that separate they are yet joined together. -- Wei Boyang (Canton Qi - Triplex Unity)

Taoist master Shangyang comments on this:

In just these two lines is the most perfect and complete summary of what is meant here. Separate they are yet joined together meaning that the two objects Yin and Yang are 10,000 miles apart in their activity - but if they gain the old Yellow Woman to act as match-maker, although far from each other, they come very close together. And then the two materials respond in due measure, bearing as a seed ‘the primacy of yin and yang. -- Master Shangyang (The Secret of Everlasting life, Commentary on the CanTong Qi)

Now these twelve hexagrams are seen from a different perspective. The two groups of six hexagram (six hexagrams of advancing Yang and six of advancing Yin), if they gain the Yellow Woman, actually represent the inhalation and exhalation of the six yang breaths of the firing process.

The rising and descending of exhalation and inhalation in alternate succession corresponds to the relationship of yin and yang. 
-- The Cultivation of Realization, by an unknown author

The true fire is one`s own spirit: the true times are one`s own breathing. Refining the medicine by means of fire in order to form the Elixir is like spirit driving breath in order to attest the Tao. -- Zhu Yuanyu 17th c. Taoist master, Commentary on the Cantong Qi
Ancient immortals used the term Golden Pill (Elixir) as a metaphor of the essence of true consciousness, which is fundamentally complete and illumined. Growing from one yang ䷗ to gradually reach the pure wholeness of six yangs ䷀, going from vague to clear, the Gold Elixir develops naturally. -- Liu Yiming, The Inner Teachings of Taoism

This poem about the Sword of Wisdom shows the same idea. The six yangs and six yins are the inhalation and exhalation of the six breaths of the firing process.

The Sword of Wisdom

From the Book of Balance and Harmony, by Li Dao Chun 13th c. Taoist master

Ever since adepts handed on
the secret of the sword,
The true imperative has been upheld
Completely, truly adamant.

When students of the Tao
Know this secret,
The yang spirit is intensely powerful,
And the yin demons vanish.

The subtle function of spiritual work
Is truly hard to measure;
I now give an explanation for you.
In telling you about it,
I divulge the celestial mechanism.

Setting to work when one yang returns,
First have the six yangs pump the furnace bellows;
Then the six yins work the tongs and hammer.
When the work of firing is complete,
it produces the sword.

This precious sword fundamentally has no form;
The name is set up because it has spiritual effect.
Learning the Tao and practicing reality
Depend on this sword;
Without this sword,
the Tao cannot be achieved.

The last six of the Twelve Sovereign Hexagrams, in which yin energy grows and yang energy retreats. (click to enlarge)

The last six of the Twelve Sovereign Hexagrams, in which yin energy grows and yang energy retreats. (click to enlarge)

The crescent moon, representing the return
of yang light.

The balance of yin - Shakti and yang - Shiva (18th c. Indian gouache)

The mind of Tao is upside down;
no new buds can be generated.
(Tarot card XII, The hanged Man)

Venus of Willendorf, estimated to have been carved .24,000–22,000 BCE. She is a symbol of the Earth Mother or Mother Goddess that can be found in all esoteric traditions. In Taoism she is called the Yellow Woman
or the Mysterious Female.

Fudō Myo-o - the immovable King of Light holding a six-pointed Vajra sword
(by Ukei, Ganjojuin temple, Shizuoka, Japan)

Christ with sword, Archiepiscopal Chapel, Ravenna, 5th C AD.

Think not that I am come to send peace on earth. I came not to send peace, but a sword.
-- The Bible, The Gospel of Matthew, 10:34