First the definitions
The twelve branches combine in fixed ways: liu-he is six pairwise combinations (Zi-Chou, Yin-Hai, Mao-Xu, Chen-You, Si-Shen, Wu-Wei); san-he is four triads (Shen-Zi-Chen, Hai-Mao-Wei, Yin-Wu-Xu, Si-You-Chou) where any two members count as a san-he pair; san-hui groups the three branches of each season (Yin-Mao-Chen, Si-Wu-Wei, Shen-You-Xu, Hai-Zi-Chou). Liu-chong is the six opposite pairs (Zi-Wu, Chou-Wei, Yin-Shen, Mao-You, Chen-Xu, Si-Hai); liu-hai arises when a liu-he pair is broken by a clash; xing comes in four groups, with Chen-Wu-You-Hai as the self-penalty set. To find the branch of any day, use the perpetual lunar calendar.
The master table
| 生肖Animal | 六合Liu-he | 三合San-he | 三会San-hui | 六冲Liu-chong | 六害Liu-hai | 相刑Xing |
|---|---|---|---|---|---|---|
| 鼠（子） | 牛 | 猴、龙（水局） | 猪、牛（水会） | 马 | 羊 | 兔（无礼之刑） |
| 牛（丑） | 鼠 | 蛇、鸡（金局） | 猪、鼠（水会） | 羊 | 马 | 狗、羊（恃势之刑） |
| 虎（寅） | 猪 | 马、狗（火局） | 兔、龙（木会） | 猴 | 蛇 | 蛇、猴（无恩之刑） |
| 兔（卯） | 狗 | 猪、羊（木局） | 虎、龙（木会） | 鸡 | 龙 | 鼠（无礼之刑） |
| 龙（辰） | 鸡 | 猴、鼠（水局） | 虎、兔（木会） | 狗 | 兔 | 马、鸡、猪（自刑） |
| 蛇（巳） | 猴 | 鸡、牛（金局） | 马、羊（火会） | 猪 | 虎 | 虎、猴（无恩之刑） |
| 马（午） | 羊 | 虎、狗（火局） | 蛇、羊（火会） | 鼠 | 牛 | 龙、鸡、猪（自刑） |
| 羊（未） | 马 | 猪、兔（木局） | 蛇、马（火会） | 牛 | 鼠 | 牛、狗（恃势之刑） |
| 猴（申） | 蛇 | 鼠、龙（水局） | 鸡、狗（金会） | 虎 | 猪 | 虎、蛇（无恩之刑） |
| 鸡（酉） | 龙 | 蛇、牛（金局） | 猴、狗（金会） | 兔 | 狗 | 龙、马、猪（自刑） |
| 狗（戌） | 兔 | 虎、马（火局） | 猴、鸡（金会） | 龙 | 鸡 | 牛、羊（恃势之刑） |
| 猪（亥） | 虎 | 兔、羊（木局） | 鼠、牛（水会） | 蛇 | 猴 | 龙、马、鸡（自刑） |
自刑指同组内地支之间的自我惩罚关系：辰午酉亥四个地支两两相刑（如龙与马、龙与鸡互为自刑对象）。表中相刑列对自刑组列出其余三个成员。The self-penalty group covers Chen, Wu, You and Hai: those four branches penalise one another pairwise (e.g. Dragon with Horse or Rooster). The Xing column lists the other members of the group.
Reading liu-he and san-he
Liu-he pairs two branches: Zi-Chou turns to earth, Yin-Hai to wood, Mao-Xu to fire, Chen-You to metal, Si-Shen to water and Wu-Wei to earth — the bracketed element is the traditional “transformed qi” of the pair. San-he builds triads: Shen-Zi-Chen forms the water frame, Hai-Mao-Wei wood, Yin-Wu-Xu fire and Si-You-Chou metal, and any two members of a triad are read as a san-he pair. San-hui gathers each season: Yin-Mao-Chen meets east-wood, Si-Wu-Wei south-fire, Shen-You-Xu west-metal, Hai-Zi-Chou north-water. Every pairing can be checked branch by branch on the <a href="ganzhi.html">60 Jiazi page</a>.
Clashes, harms and penalties: where they come from
Liu-chong mirrors opposite positions on the direction circle: Zi (north) clashes Wu (south), Mao (east) clashes You (west), and so on — the two branches sit six steps apart. Liu-hai traditionally arises when a liu-he pair is broken: if Wu clashes Zi away from Chou, then Zi and Wei become “harms”. Xing is the most intricate: three pairwise sets (Yin-Si-Shen “ungrateful”, Chou-Xu-Wei “presumptuous”, Zi-Mao “discourteous”) plus the self-penalty set Chen-Wu-You-Hai, whose members penalise one another.
Related tools
For your animal and star sign by birthday, use the zodiac lookup; for any day’s branch, the perpetual lunar calendar; for stems, branches, elements and na-yin, the 60 Jiazi table; for lunar festival dates, the festival reference.
FAQ
What do liu-he and san-he mean?
They are fixed combination rules among the twelve branches: six pairwise pairs, and four triads. The page states the correspondences and their transformed elements; how to interpret them is a separate system outside its scope.
Does a clash mean two people should not marry?
“Clashing animals should not marry” is folklore. The page lists the liu-chong correspondences as they are, without endorsing any verdict of good or bad luck. Whether a marriage works depends on how the two people treat each other, their values and circumstances — plenty of “clashing” couples are happily married. Treat this page as cultural reference material.
Why are Dragon, Horse, Rooster and Pig “self-penalising”?
Tradition groups Chen, Wu, You and Hai as the self-penalty set: members penalise one another pairwise, structurally different from the three pairwise sets. It is a fixed grouping of the branch system, listed here as tradition states it.
Does the New Year vs Lichun switch affect the table?
No. The relations are built on the twelve branches. Whether you switch animals at lunar New Year or Lichun, only birthdays on the boundary days differ; once the animal is fixed, its liu-he, san-he and clash relations are unique. The <a href="zodiac.html">zodiac lookup</a> shows both conventions.