Hexagram pairs in the I Ching: why the 64 come in twos

The 64 hexagrams of the received I Ching are arranged in 32 pairs. In 28 of them, the second hexagram is the first turned upside down; in the remaining 4, where turning the figure over changes nothing, the second is the first with every line reversed. Reading a hexagram together with its partner is one of the simplest ways to see what it is really about, because each pair is built around a single contrast.

The rule behind the pairs

Take any hexagram and rotate it 180 degrees, so that the top line becomes the bottom. For most figures you get a different hexagram: Hexagram 3, Zhun, turned over, is Hexagram 4, Meng. Hexagrams 3 and 4 stand next to each other in the sequence, and so does every such couple — 5 and 6, 7 and 8, all the way to 63 and 64. Later tradition calls this relation 綜 (zong, "woven") or 覆 (fu, "overturned").

Eight hexagrams look the same upside down: 1 Qian, 2 Kun, 27 Yi, 28 Da Guo, 29 Kan, 30 Li, 61 Zhong Fu and 62 Xiao Guo. They cannot be paired by turning, so they are paired by reversal: every yang line becomes yin and every yin line yang (錯, cuo, or 變, bian). That gives the four "opposite" pairs:

• 1 Qian and 2 Kun — all yang, all yin.
• 27 Yi (Nourishment) and 28 Da Guo (Great Excess) — a hollow mouth and an overloaded beam.
• 29 Kan and 30 Li — water and fire, the pit and the clinging flame.
• 61 Zhong Fu (Inner Truth) and 62 Xiao Guo (Small Excess).

The Tang scholar Kong Yingda (孔穎達) put the whole rule in eight characters in his subcommentary on the Xugua: 二二相耦，非覆即變 — "they pair two by two; if not overturned, then reversed." 28 + 4 = 32 pairs, and no hexagram is left over. You can explore the same operations on any figure in our guide to nuclear, inverse and opposite hexagrams; here the focus is on the pairs as the sequence actually uses them.

The four pairs that are both

Four of the turned-over pairs are special: turning the figure over also reverses every line. They are 11 and 12, 17 and 18, 53 and 54, and 63 and 64. In these, the partner is both the inverse and the opposite at once, and the contrast is sharpest of all.

Tai and Pi: one picture, two directions

Hexagram 11, Tai puts heaven below and earth above. Heaven rises, earth sinks, and the two meet: the Judgment says 小往大來，吉亨 — "the small departs, the great approaches; good fortune, success." Turn it over and you have Hexagram 12, Pi: heaven above, earth below, each moving away from the other. Its Judgment reverses the phrase: 大往小來 — "the great departs, the small approaches."

Read as a pair, the two hexagrams are not "good" and "bad" but the two phases of one cycle. Tai already warns, in its third line, 無平不陂，無往不復 — "no level without a slope, no going without a return" — and its top line has the city wall falling back into the moat. Pi, for its part, ends with 傾否，先否後喜 — "the standstill is overturned; first obstruction, then joy." The Xugua spells out the link: 泰者，通也。物不可以終通，故受之以否 — "Tai means flowing through; things cannot flow forever, so Pi follows." If you cast Tai, its partner reminds you that openness is a phase to use well, not a permanent state; if you cast Pi, its partner shows what the blockage is waiting to become.

Pairs and the two halves of the book

The pairs also frame the whole text. The upper canon (1–30) opens with Qian and Kun and closes with Kan and Li — both opposite pairs. The lower canon (31–64) opens with 31 Xian and 32 Heng, Attraction and Duration, and closes with Ji Ji and Wei Ji. The Zagua's verdict on Xian and Heng is a single contrast: quickness and lastingness. In the Ming dynasty, Lai Zhide (來知德) made 錯綜 — reversal and overturning — the centre of his commentary, insisting that every hexagram be read together with its partners; his detailed method differs from Zhu Xi's.

Ji Ji and Wei Ji: the pair that ends the book

Hexagram 63, Ji Ji, "After Completion", has every line in its proper place — yang in the odd positions, yin in the even. Hexagram 64, Wei Ji, "Before Completion", has every line out of place. One is the other turned over and also the other reversed.

Look at how the line texts mirror each other. Turning a hexagram over moves line 1 to position 6, line 2 to 5, line 3 to 4. Ji Ji's first line "wets its tail"; Wei Ji's sixth line "wets its head". Ji Ji's sixth line wets its head; Wei Ji's first line wets its tail. Ji Ji's third line has the Gaozong king attacking the Guifang for three years; Wei Ji's fourth line repeats the campaign and the three years. The authors of the text clearly composed these two as a pair.

Their meaning as a pair is one of the most quoted teachings of the book: completion is already the beginning of disorder (Ji Ji's Judgment ends 初吉終亂, "good fortune at first, disorder at the end"), and incompletion still holds promise. The canon closes on Wei Ji, not Ji Ji — the book itself ends open.

Echoes in the line texts

The mirroring is not limited to 63 and 64. Some lines are verbally identical across a pair, in exactly the mirrored position:

• Hexagram 41, Sun, line 5, and Hexagram 42, Yi, line 2, share the phrase about a gift of tortoise shells worth ten strings of cowries that cannot be refused.
• Hexagram 43, Guai, line 4, and Hexagram 44, Gou, line 3, share the image of thighs without skin and a halting walk.

Because the inverse puts line 4 of one figure at line 3 of the other, and line 5 at line 2, these are the "same" line seen from the other end. When you get one of them as a moving line, reading its twin in the partner hexagram is a natural cross-check.

What the pairs do and do not mean for a reading

The Zagua commentary (see the Xugua and Zagua) reads the sequence almost entirely in pairs, giving each couple a contrasting tag: 否泰，反其類也 — "Pi and Tai are opposite in kind"; 損益，盛衰之始也 — "Decrease and Increase are the beginnings of flourishing and decline." That is a strong hint from within the tradition that a hexagram's partner belongs to its meaning.

But be careful about what the pairing is not. The partner is not a second answer, and it is not the hexagram your situation changes into — that is the changed hexagram, which depends on your moving lines. Classical divination rules (Zhu Xi's included) do not tell you to read the partner at all; using it is an interpretive aid that many modern readers find helpful. For the broader logic of the order, see our guide to the King Wen sequence.

How to use the pairs when you read a cast

• Find the partner. If your hexagram has an odd number, its partner is the next one; if even, the previous one.
• Name the contrast. Ask what single difference separates the two: rising and falling, gathering and dispersing, decreasing and increasing. That contrast is usually the heart of your hexagram.
• Turn the figure for the other side. An inverse partner is the same six lines seen from the opposite end. If your question involves another person, the partner can be a useful picture of how the situation looks from where they stand.
• Check the mirrored line. If you have a moving line at position n, glance at line 7 − n in the partner hexagram (for the four opposite pairs, the same position).
• Keep the primary reading primary. Write your answer from your own hexagram and moving lines first; use the partner only to sharpen it.

When you cast a reading, the hexagram pages in the library let you step to the neighbouring hexagram in one click, which is all you need to read a pair.