I Ching Related Hexagrams (易經互錯綜交卦)

Read a Hexagram in Depth — Through Its Four Transformations

Overview

In the I Ching, a hexagram is never read entirely on its own. The classical way to read one in depth is to read it together with its transformations — the related hexagrams hidden inside and around it. This endpoint takes any of the 64 hexagrams and derives the four classical relatives that every serious commentary consults: the 互卦 (nuclear hexagram), the 錯卦 (opposite hexagram), the 綜卦 (reversed hexagram) and the 交卦 (swapped hexagram), plus the 之卦 (changing hexagram) if there are moving lines. Together they turn a single symbol into a small map of a situation — its surface, its hidden core, its shadow, the view from the other side, and where it is heading.

Origin & history

The technique is as old as the structured study of the I Ching itself. The 互卦 (nuclear or 'mutual' hexagram) is discussed in the Ten Wings and was central to Han-dynasty commentators such as Jing Fang and later to Yu Fan, who used the inner lines of a hexagram to reveal a hidden second hexagram. The pairing of hexagrams by 綜 (reversal) is the very principle that orders the King Wen sequence — the received order of the 64 hexagrams — in which almost every adjacent pair is one hexagram turned upside-down. The 錯 (lateral/opposite) relationship, in which every line is inverted, and the 交 (trigram-swap) relationship complete the set of transformations by which a hexagram is read against its complements.

These four relationships remain standard in both scholarly and divinatory practice. A diviner who casts a hexagram will routinely check its nuclear hexagram for the inner dynamic of the matter, its reversed hexagram for how the situation looks from the other party's standpoint, and its opposite hexagram for the complementary or repressed side. The King Wen sequence encodes the reversal pairing directly: of the 32 pairs, 28 are 綜 pairs (each hexagram the upside-down image of its neighbour) and only four are 錯 pairs — the eight hexagrams that look the same upside-down (乾, 坤, 頤, 大過, 坎, 離, 中孚, 小過), whose partners are therefore their line-for-line opposites. askTIAN's engine reproduces this structure exactly, and flags the line-symmetric cases where the reversed hexagram is the hexagram itself.

How it works

Give a hexagram as a King Wen number (1–64) or as six lines from bottom to top (1 = yang, 0 = yin, e.g. 111111 = 乾), and optionally the positions of any moving lines. The engine computes each transformation by a simple, exact operation on the six lines: the 錯卦 inverts every line; the 綜卦 reverses their order (turning the hexagram upside-down); the 互卦 takes lines 2·3·4 as its lower trigram and lines 3·4·5 as its upper; and the 交卦 exchanges the upper and lower trigrams. Each resulting hexagram is looked up in the standard King Wen sequence and returned with its number, name, six lines, glyphs and trigram breakdown. If moving lines are supplied, the 之卦 (the hexagram they change the situation into) is returned as well. Because these are exact transformations, the results are fully deterministic.

Good for

• Reading a cast hexagram in depth, not in isolation
• The 互卦 (nuclear) — the hidden inner process of a situation
• The 錯卦 (opposite) — the complementary or repressed side
• The 綜卦 (reversed) — how it looks from the other party's view
• The 交卦 (swapped) — the situation with its two forces reversed
• Following moving lines to the 之卦 (changing hexagram)

Use cases

Deepen a Divination

After casting a hexagram (via coin toss, yarrow, Liuyao or Meihua), pass its number to get the four related hexagrams that classical practice consults to read the situation fully.

The Nuclear Hexagram

Get the 互卦 built from the inner lines — the hidden process unfolding at the heart of the matter, between its beginning and its end.

Both Sides of a Situation

The 綜卦 shows the other party's viewpoint and the 錯卦 the complementary shadow — together they round out a one-sided reading.

Follow the Change

Supply moving-line positions to receive the 之卦, the hexagram the situation is transforming into.

Key terms

互卦 (Nuclear / Mutual)

The hexagram formed by taking the original's lines 2·3·4 as the lower trigram and lines 3·4·5 as the upper — the hidden inner process at the core of the situation.

錯卦 (Opposite / Lateral)

Every line inverted (yin↔yang) — the complementary shadow, the same situation seen from the exact opposite standpoint.

綜卦 (Reversed / Overturned)

The hexagram turned upside-down (line order reversed) — the view from the other party's side, or the next stage once the situation turns over. This is the pairing that orders the King Wen sequence.

交卦 (Swapped)

The upper and lower trigrams exchanged — the situation with its two forces trading places.

之卦 (Changing)

The hexagram that the moving lines transform the original into — where the situation is heading.

API

The askTIAN I Ching Related Hexagrams endpoint takes a hexagram (a King Wen number or six lines) and returns its four classical transformations — 互 (nuclear), 錯 (opposite), 綜 (reversed) and 交 (swapped) — plus the 之卦 from any moving lines. Each related hexagram comes back with its King Wen number, name (Chinese, pinyin and English), six lines, line-stack glyphs and upper/lower trigrams; the primary hexagram also carries the five-element relationship between its trigrams. The transformations are exact deterministic operations on the standard King Wen sequence, gold-locked by structural invariants (the 綜-pair sequence, the eight line-symmetric hexagrams, and the involution of 錯/綜/交). A best-effort LLM reading is returned in parsable sections (set interpretation:false for structured data only). Honest rails: the transformations are exact, but the interpretive meanings are a traditional framework, not a validated predictor, and not medical, legal or financial advice.

Endpoint: POST /trpc/iching.relations — 3 TIAN Points. See the API documentation and Playground.