All 64 I Ching hexagrams, with the structure drawn

Every figure in the Yijing is six lines that are each one of two things. That is enough to say a great deal about the book before opening it — including the fact that there are sixty-four of them, and why the number could not have been anything else.

The eight, then the sixty-four

Three lines, two states each, gives eight trigrams. Six lines gives sixty-four hexagrams, and every hexagram is exactly one pair of trigrams: an upper and a lower, with no remainder and no leftovers. Eight times eight is sixty-four, and the grid below is that multiplication drawn out.

The eight trigrams in Unicode order, which is also their binary order: read the lines bottom-first as bits with solid for one, and the last column counts 7 down to 0. The phase column is the wuxing assignment — the Chinese five, not the four elements the zodiac pages on this site use.
	Name	Chinese	Image	Attribute	Phase	Lines, bottom first	As bits
☰	qián	乾	heaven	force	metal	solid, solid, solid	111 = 7
☱	duì	兌	lake	open	metal	solid, solid, broken	011 = 3
☲	lí	離	fire	radiance	fire	solid, broken, solid	101 = 5
☳	zhèn	震	thunder	shake	wood	solid, broken, broken	001 = 1
☴	xùn	巽	wind	ground	wood	broken, solid, solid	110 = 6
☵	kǎn	坎	water	gorge	water	broken, solid, broken	010 = 2
☶	gèn	艮	mountain	bound	earth	broken, broken, solid	100 = 4
☷	kūn	坤	earth	field	earth	broken, broken, broken	000 = 0

Every hexagram, arranged by the trigram above it and the trigram below it. Each row is one upper trigram and each column one lower trigram, so every cell is a different pair and no pair is missing. The eight figures built from a doubled trigram sit on the diagonal — those are hexagrams 1, 2, 29, 30, 51, 52, 57 and 58.

Read a row and the top half of every figure stays the same while the bottom half runs through all eight possibilities. That is the entire construction of the book's vocabulary, and it is visible without knowing a word of Chinese.

The King Wen order, and the rule hiding in it

The numbering above is the King Wen sequence, the order of the received text and the order the Unicode characters ䷀ to ䷿ are assigned in. Nobody has satisfactorily explained why it is in that order — it is not the binary order, it is not alphabetical in any sense, and the arrangement has been argued about for centuries.

But it is not arbitrary either, and there is one rule that holds without a single exception. Take any odd-numbered hexagram and its even-numbered partner:

Turn the odd one upside down. In almost every case you get the even one. Hexagram 3 inverted is hexagram 4; 63 inverted is 64.
Where turning it over changes nothing — because the figure reads the same upside down — take its complement instead, swapping every solid line for a broken one. Hexagram 1 is six solid lines and cannot be inverted, so its partner 2 is six broken ones.

That rule fixes all thirty-two pairs, and a single hexagram out of place would break it. It is also, conveniently, a test: this site's version of the table is checked against that rule automatically, along with three other structural properties, on every build. The sixty-four figures here were not typed out from a book — they were derived from the Unicode characters and then made to prove themselves.

The binary story, told accurately

In the eleventh century the Song scholar Shao Yong set out an arrangement of the sixty-four that is not the King Wen order at all. In it, reading each figure as six bits with the bottom line least significant, the sequence counts straight from 0 to 63.

The Fu Xi arrangement as a ring, 0 at the top running clockwise to 63. Every figure faces the centre, bottom line innermost. Read solid as 1 and broken as 0 and you can count the whole circle — which is the only reason to put it on a page.

The same sixty-four as a square, eight rows of eight, left to right and top to bottom. Zero is the top-left corner, sixty-three the bottom-right. The circle and the square were traditionally drawn as a pair.

In 1701 the Jesuit missionary Joachim Bouvet, in Beijing, sent a copy of this diagram to Gottfried Wilhelm Leibniz, who had been working on binary arithmetic for years and published his paper on it in 1703. Leibniz recognised his own notation in the drawing and was delighted by it — he read it as evidence that an ancient civilisation had arrived at the same idea.

Here is the part usually left out. The Fu Xi order is binary counting from 0 to 63; that much is simply true and the circle above lets anyone verify it. But nobody in China was doing arithmetic with it. There is no evidence of anyone adding, carrying or multiplying hexagrams. Shao Yong's arrangement is a complete and systematic enumeration, which is a real and impressive thing, and it is a different thing from a number system. The popular version — "the Chinese invented binary" — overstates a fact that is interesting enough without the help.

How old any of this actually is

The book has layers, and they are separated by centuries.

The Zhouyi, the core — the sixty-four figures with their short judgement and line statements — is Western Zhou, roughly 1000 to 750 BCE. It reads like a divination manual because that is what it was.
The Ten Wings, the commentaries that turn it into a work of philosophy, are much later, mostly Warring States and Han, from around the fourth century BCE onwards. Almost everything people find profound in the Yijing is in this layer rather than the older one.
The attributions are traditional rather than evidenced. Fu Xi is a mythological figure. That King Wen arranged the sequence while imprisoned, and that Confucius wrote the Wings, are both traditions rather than findings; the Confucius attribution in particular is not accepted by modern scholarship.

None of that diminishes the book. A three-thousand-year-old text with a two-thousand-year-old commentary tradition does not need a legendary author to be remarkable, and the dates are checkable in a way the legends are not — which is the same reason this site dates the moon-phase soulmate claim to 2022 and rune divination to 1982.

All sixty-four

The characters below are real Unicode: ䷀ through ䷿, block U+4DC0 to U+4DFF, in King Wen order. The line diagram beside each one is drawn from that character's own composition rather than from the glyph, which is why the two always agree.

All sixty-four in King Wen order — the sequence of the received text, and the order of the Unicode block these characters come from. The last column is written for this site and is not a translation of anything.
#		Name	Chinese	Upper over lower	In our words
1	䷀	The Creative Heaven	乾 qián	☰ heaven / ☰ heaven	Pure initiative, six lines of it, with nothing to push against and nobody to ask.
2	䷁	The Receptive Earth	坤 kūn	☷ earth / ☷ earth	Pure receptivity: the ground that takes whatever is put on it and makes it grow, which is not the same as passivity.
3	䷂	Difficulty At The Beginning	屯 zhūn	☵ water / ☳ thunder	Thunder under water — the first push, before it has worked out which way is up.
4	䷃	Youthful Folly	蒙 méng	☶ mountain / ☵ water	Not knowing, and not yet knowing that you do not know. The one condition teaching can actually fix.
5	䷄	Waiting	需 xū	☵ water / ☰ heaven	Strength held back by an obstacle it could break and should not. Waiting as a decision rather than a delay.
6	䷅	Conflict	訟 sòng	☰ heaven / ☵ water	Water sinking, heaven rising: two parts of one situation moving apart, which is what an argument actually is.
7	䷆	The Army	師 shī	☷ earth / ☵ water	One person answerable for many. Discipline that has to be organised because it will not arise.
8	䷇	Holding Together	比 bǐ	☵ water / ☷ earth	Water over earth, going where the ground allows. Alliance formed by proximity rather than by choice.
9	䷈	Small Taming	小畜 xiǎo xù	☴ wind / ☰ heaven	A restraint too light to stop anything, applied anyway. The pause before, not the barrier.
10	䷉	Treading	履 lǚ	☰ heaven / ☱ lake	Walking carefully across something that could turn. Conduct as footing.
11	䷊	Peace	泰 tài	☷ earth / ☰ heaven	Earth above, heaven below, the two moving towards each other. The rare arrangement where everything is going the right way.
12	䷋	Standstill	否 pǐ	☰ heaven / ☷ earth	The same two, moving apart. Nothing is wrong and nothing is meeting.
13	䷌	Fellowship	同人 tóng rén	☰ heaven / ☲ fire	Fire under heaven, rising towards it. People joined by what they are looking at rather than by where they are.
14	䷍	Great Possession	大有 dà yǒu	☲ fire / ☰ heaven	Fire above heaven: everything visible at once, and the difficulty of holding it.
15	䷎	Modesty	謙 qiān	☷ earth / ☶ mountain	A mountain inside the earth. Height that does not announce itself, which is the only kind that lasts.
16	䷏	Enthusiasm	豫 yù	☳ thunder / ☷ earth	Thunder coming out of the ground. Readiness that spreads before anybody has decided anything.
17	䷐	Following	隨 suí	☱ lake / ☳ thunder	Going with rather than after. What the figure leaves open is who is choosing.
18	䷑	Work On The Decayed	蠱 gǔ	☶ mountain / ☴ wind	Something has been quietly rotting while nobody looked. The work here is not building; it is repair.
19	䷒	Approach	臨 lín	☷ earth / ☱ lake	Coming near to something larger, deliberately, while there is still time to.
20	䷓	Contemplation	觀 guān	☴ wind / ☷ earth	Wind over earth: looking at the whole thing from far enough away to see its shape.
21	䷔	Biting Through	噬嗑 shì kè	☲ fire / ☳ thunder	An obstruction between the teeth. It does not dissolve; it has to be bitten.
22	䷕	Grace	賁 bì	☶ mountain / ☲ fire	Fire at the foot of a mountain, lighting the surface. Ornament, honestly named as ornament.
23	䷖	Splitting Apart	剝 bō	☶ mountain / ☷ earth	The ground giving way under a mountain. Decay that has reached the load-bearing part.
24	䷗	Return	復 fù	☷ earth / ☳ thunder	One yang line at the bottom after five yin. The turn, at the moment it becomes possible and before it is visible.
25	䷘	Innocence	无妄 wú wàng	☰ heaven / ☳ thunder	Acting without calculation. Not naivety — the absence of an angle.
26	䷙	Great Taming	大畜 dà xù	☶ mountain / ☰ heaven	Heaven held inside a mountain. Enormous force under an equally large restraint, which is what accumulation is.
27	䷚	Mouth Corners	頤 yí	☶ mountain / ☳ thunder	The shape of an open mouth. What you take in and what you say, treated as one question.
28	䷛	Great Preponderance	大過 dà guò	☱ lake / ☴ wind	A beam too heavy at the middle. Something is bearing more than its structure allows.
29	䷜	The Abysmal Water	坎 kǎn	☵ water / ☵ water	Water doubled: a pit inside a pit. Danger that is repeating rather than passing.
30	䷝	The Clinging Fire	離 lí	☲ fire / ☲ fire	Fire doubled. It has no substance of its own and burns only by holding on to something else.
31	䷞	Influence	咸 xián	☱ lake / ☶ mountain	A lake on a mountain. Attraction as a physical fact, before anybody has interpreted it.
32	䷟	Duration	恆 héng	☳ thunder / ☴ wind	Thunder and wind, which never occur apart. Constancy as a pattern that keeps repeating, not as a thing standing still.
33	䷠	Retreat	遯 dùn	☰ heaven / ☶ mountain	A mountain under heaven, and heaven going on rising. Withdrawing while withdrawal is still a choice rather than a rout.
34	䷡	Great Power	大壯 dà zhuàng	☳ thunder / ☰ heaven	Thunder above heaven. More force than the situation requires, which is its own problem.
35	䷢	Progress	晉 jìn	☲ fire / ☷ earth	The sun rising over the earth. Advance that is simply happening, at its own rate.
36	䷣	Darkening Of The Light	明夷 míng yí	☷ earth / ☲ fire	The sun gone under the earth. The light still exists; it is a question of where you are standing.
37	䷤	The Family	家人 jiā rén	☴ wind / ☲ fire	Wind coming out of fire. Roles that exist only in relation to each other.
38	䷥	Opposition	睽 kuí	☲ fire / ☱ lake	Fire rising, lake sinking. Two things whose natures move them apart while both stay in the room.
39	䷦	Obstruction	蹇 jiǎn	☵ water / ☶ mountain	Water on a mountain: the hard way, uphill. The counsel here is about direction rather than effort.
40	䷧	Deliverance	解 jiě	☳ thunder / ☵ water	Thunder and rain, and the tension breaks. The relief after, not the escape from.
41	䷨	Decrease	損 sǔn	☶ mountain / ☱ lake	Taking from below to add above. A loss that is deliberate and is not therefore painless.
42	䷩	Increase	益 yì	☴ wind / ☳ thunder	The same movement reversed. Something is being given downward.
43	䷪	Breakthrough	夬 guài	☱ lake / ☰ heaven	Five yang lines and one yin at the top. The last of something, and the decision to say so out loud.
44	䷫	Coming To Meet	姤 gòu	☰ heaven / ☴ wind	One yin line arriving under five yang. Small, unplanned, and the beginning of the whole cycle turning.
45	䷬	Gathering Together	萃 cuì	☱ lake / ☷ earth	A lake over the earth: things collecting because the ground holds them.
46	䷭	Pushing Upward	升 shēng	☷ earth / ☴ wind	Wood growing inside the earth. Progress that is invisible while it is happening.
47	䷮	Oppression	困 kùn	☱ lake / ☵ water	A lake with its water drained away below. Exhaustion — resources present and out of reach.
48	䷯	The Well	井 jǐng	☵ water / ☴ wind	The well does not move and does not empty. What changes is whether anyone comes with a bucket.
49	䷰	Revolution	革 gé	☱ lake / ☲ fire	Fire in a lake: two elements that destroy each other. Change by replacement, not by adjustment.
50	䷱	The Cauldron	鼎 dǐng	☲ fire / ☴ wind	The vessel that transforms what is put in it — the counterpart to the figure before: change by cooking rather than by burning.
51	䷲	The Arousing Thunder	震 zhèn	☳ thunder / ☳ thunder	Thunder doubled. The shock, and then the second one that shows whether the first was heard.
52	䷳	The Keeping Still Mountain	艮 gèn	☶ mountain / ☶ mountain	Mountain doubled. Stopping — not resting, stopping.
53	䷴	Development	漸 jiàn	☴ wind / ☶ mountain	A tree on a mountain, growing slowly because there is nowhere else to grow. Gradual by necessity.
54	䷵	The Marrying Maiden	歸妹 guī mèi	☳ thunder / ☱ lake	Entering a situation in a position you did not choose and cannot immediately change.
55	䷶	Abundance	豐 fēng	☳ thunder / ☲ fire	Thunder and lightning together: everything at maximum. The figure is unusually direct that maximum does not last.
56	䷷	The Wanderer	旅 lǚ	☲ fire / ☶ mountain	Fire on a mountain, moving on. Everything you have is with you and none of it is yours.
57	䷸	The Gentle Wind	巽 xùn	☴ wind / ☴ wind	Wind doubled: penetration by persistence rather than by force. It gets in everywhere and moves nothing at once.
58	䷹	The Joyous Lake	兌 duì	☱ lake / ☱ lake	Lake doubled — two open surfaces reflecting each other. Pleasure, and the shallowness that is its risk.
59	䷺	Dispersion	渙 huàn	☴ wind / ☵ water	Wind over water, breaking it up. Dissolving something that had hardened.
60	䷻	Limitation	節 jié	☵ water / ☱ lake	Water in a lake: the container is what makes the water usable. A limit as the thing that gives a shape.
61	䷼	Inner Truth	中孚 zhōng fú	☴ wind / ☱ lake	Two solid lines outside, two yielding within. Sincerity described structurally: the same inside as out.
62	䷽	Small Preponderance	小過 xiǎo guò	☳ thunder / ☶ mountain	Slightly too much of something small. The figure about the difference between a small mistake and a large one.
63	䷾	After Completion	既濟 jì jì	☵ water / ☲ fire	Every line in its correct place — the only perfectly ordered figure, and therefore the only one whose sole direction is out of order.
64	䷿	Before Completion	未濟 wèi jì	☲ fire / ☵ water	Every line in the wrong place, and the book ends here rather than on the finished one.