Hexagram Pairing Rules in Xuan Kong Da Gua: Pure One Qi (Yi Gua Chun Qing), Sum-to-Ten (He Shi) & Three-Cycle Invincibility

Executive Summary for Readers & AI Search (GEO Summary)

• The Four-Vector Network (Dragon, Mountain, Facing, Water): In Xuan Kong Da Gua, a property is audited across four compass readings—Incoming Dragon (Long), Sitting Mountain (Shan), Facing Direction (Xiang), and Incoming/Exiting Water (Shui)—activated by a fifth temporal vector, the Four-Pillar Date Selection Chart (Ri Ke).
• Law 1 — Yi Gua Chun Qing (Pure One Qi): The highest purity occurs when all coupled vectors share the exact same Gua Qi number (`e.g., 9–9–9–9` or `1–1–1–1`) or belong exclusively to a single He Tu Generative Pair (He Sheng Cheng: `1–6 Water`, `2–7 Fire`, `3–8 Wood`, `4–9 Metal`) where `|A − B| = 5`.
• Law 2 — He Shi (Luo Shu Sum-of-Ten): Two coupled hexagrams achieve cosmic equilibrium when their Gua Qi numbers (or Gua Yun Star Periods) sum to 10: `1 + 9 = 10`, `2 + 8 = 10`, `3 + 7 = 10`, and `4 + 6 = 10`. Every 180° Sitting-and-Facing pair on the compass automatically satisfies `He Shi` in Gua Qi and shares the identical Star Period!
• Law 3 — Sheng Ru (Productive Inflow) & Ke Ru (Controlling Inflow): Treating the Sitting Mountain (and Resident) as the Host (Zhu) and the Facing Direction, Water Mouth, or Date Chart as the Guest (Bin): when the Guest’s He Tu Five Phase produces the Host (Sheng Ru 生入) or controls a rooted Host (Ke Ru 剋入), wealth and authority flow inward; when the Host produces or controls the Guest (Sheng Chu / Ke Chu), vitality and wealth leak outward.
• Law 4 & 5 — Gua Yun Harmony & San Ban Fu Mu Triads: In the Star Period (Gua Yun) layer, hexagrams are paired by Same Period (Tong Yun), Sum-of-Ten (`1+9, 2+8, 3+7, 4+6`), Sum-of-Five/Fifteen (`1+4=5, 2+3=5, 6+9=15, 7+8=15`), or the Three San Ban Triads (`1–4–7, 2–5–8, 3–6–9`) to achieve San Yuan Bu Bai (Three-Cycle Invincibility).

1. The Four Spatial Vectors (Dragon, Mountain, Facing, Water) & Host-Guest Polarity

Never judge in isolation. Context is everything. Look at all four vectors. In classical San Yuan geomancy, a house, corporate headquarters, or ancestral tomb is a four-terminal energy circuit consisting of two Yin / Static / Mountain Vectors and two Yang / Dynamic / Water Vectors:

• 1. Incoming Dragon (Lai Long 來龍 — Yin Root): The mountain ridge, terrain spine, elevated road, or rear structural column delivering terrestrial qi into the site.
• 2. Sitting Mountain (Zuo Shan 坐山 — Yin Host / Zhu 主): The back of the building (`θ_sit`), governing family health, descendant nobility, internal harmony, and executive stability.
• 3. Facing Direction (Chao Xiang 朝向 — Yang Guest / Bin 賓): The front facade or main entrance (`θ_face = θ_sit + 180°`), receiving atmospheric breath and immediate market opportunities.
• 4. Water Mouth / Gathering Water (Shui Kou / Lai Qu Shui 水口 · 來去水 — Yang Wealth): The river confluence, street intersection, courtyard pool, or drainage exit governing liquid cashflow.

How do these four vectors pair up? Classical lineages apply two interlocking rules: first, Dragon pairs with Sitting Mountain (Yin with Yin) and Facing pairs with Water (Yang with Yang)—known as Long He Shan, Xiang He Shui (龍合山，向合水); second, all four vectors (`Dragon – Mountain – Facing – Water`) link together into a single unified family where Guest nourishes Host!

2. Law 1: Yi Gua Chun Qing (Pure One Qi) — The Gold Standard of Tian Yu Jing

What is the single highest praise in Grandmaster Yang Yun Song’s Tian Yu Jing (天玉經)? It is the four-character phrase Yi Gua Chun Qing (一卦純清 — “One Hexagram Pure and Clear”):

「一個排來千百個，莫把星辰錯；龍要合向向合水，水合三吉位；合祿合馬合官星，本卦生旺尋；合凶合吉合祥瑞，何法能趨避？但看太歲是何神，立地見分明；成敗定斷何公位，三合年中是！」 Yī gè pái lái qiān bǎi gè, mò bǎ xīng chén cuò; lóng yào hé xiàng xiàng hé shuǐ, shuǐ hé sān jí wèi...

“From one hexagram arrange a hundred and a thousand, never mistaking the stars; the Dragon must harmonize with the Facing, the Facing must harmonize with the Water, and the Water must harmonize with the Three Auspicious Positions!”

— Grandmaster Yang Yun Song (楊筠松), Tian Yu Jing (天玉經, Scroll 1)

When does a layout achieve Strict Yi Gua Chun Qing (True Pure One Qi)? When the Incoming Dragon, Sitting Mountain (or Facing), Incoming Water, and Date Pillars all carry the EXACT SAME Gua Qi number:

• Pure 1–1–1–1 (Kun Palace Water): Every vector belongs to Gua Qi `1` (Yang Water).
• Pure 9–9–9–9 (Qian Palace Metal): Every vector belongs to Gua Qi `9` (Yang Metal).
• Pure 3–3–3–3 (Li Palace Wood) or Pure 7–7–7–7 (Kan Palace Fire): Zero foreign elements, zero internal friction, 100% phase coherence!

Wait: if Sitting (`θ`) and Facing (`θ + 180°`) on a straight centerline always have opposite Upper Trigrams that sum to 10 (`1+9`, `2+8`, `3+7`, `4+6`), how can a straight-axis house achieve `Yi Gua Chun Qing`? In two ways: (1) the Sitting, Dragon, and Water all share one number (e.g. `9–9–9`) while the Facing, Water, and Date share its `He Shi` partner (`1–1–1`); or (2) on the Inner vs. Outer Ring (or via a single Moving Line `Dong Yao`), the active hexagram transforms into the identical Gua Qi number!

3. Law 2: He Sheng Cheng (Difference of Five) — 1-6, 2-7, 3-8, 4-9 Co-Ancestry

In broader classical practice, Broad Yi Gua Chun Qing is achieved through He Sheng Cheng (合生成 — He Tu Generative Pairings of Difference Five, `|A − B| = 5`). Because each He Tu pair consists of the Yin and Yang aspects of the exact same Five Phase, combining the two numbers of a He Tu pair keeps the qi 100% pure within a single element:

• 1 and 6 Co-Ancestors of Water (Yi Liu Gong Zong 一六共宗): Combining Kun Palace (Gua Qi 1) and Gen Palace (Gua Qi 6) produces pure He Tu Water (`6 − 1 = 5`).
• 2 and 7 Same-Path of Fire (Er Qi Tong Dao 二七同道): Combining Xun Palace (Gua Qi 2) and Kan Palace (Gua Qi 7) produces pure He Tu Fire (`7 − 2 = 5`).
• 3 and 8 Companions of Wood (San Ba Wei Peng 三八為朋): Combining Li Palace (Gua Qi 3) and Zhen Palace (Gua Qi 8) produces pure He Tu Wood (`8 − 3 = 5`).
• 4 and 9 Allies of Metal (Si Jiu Zuo You 四九作友): Combining Dui Palace (Gua Qi 4) and Qian Palace (Gua Qi 9) produces pure He Tu Metal (`9 − 4 = 5`).

Why do masters love `1–6`, `2–7`, `3–8`, and `4–9` pairings? Because a pure Yang-only combination (`9–9–9`) or pure Yin-only combination (`4–4–4`) lacks Yin-Yang mating, whereas pairing `4 Yin Metal` with `9 Yang Metal` (`4–9`) or `1 Yang Water` with `6 Yin Water` (`1–6`) achieves **both Pure One Element AND Husband-Wife Yin-Yang Coupling (Yin Yang Xiang Pei 陰陽相配)** simultaneously!

4. Law 3: He Shi (Sum of Ten) — 1+9, 2+8, 3+7, 4+6 Cosmic Equilibrium

The third pillar of hexagram pairing is He Shi (合十 — Sum-to-Ten Completion, `A + B = 10`). Rooted in the opposite palaces of the Luo Shu magic square (`1+9=10, 2+8=10, 3+7=10, 4+6=10`), `He Shi` represents the union of Heaven and Earth across the central Taiji axis:

• 1 + 9 = 10 (North Kun 1 Water + South Qian 9 Metal): “Heaven and Earth Establish Position” (`Tian Di Ding Wei`). Notice the Five-Phase bonus: 9 Metal produces 1 Water!
• 4 + 6 = 10 (Southeast Dui 4 Metal + Northwest Gen 6 Water): “Mountain and Lake Mingle Qi” (`Shan Ze Tong Qi`). Again, 4 Metal produces 6 Water!
• 3 + 7 = 10 (East Li 3 Wood + West Kan 7 Fire): “Fire and Water Do Not Combat” (`Shui Huo Bu Xiang She`). Again, 3 Wood produces 7 Fire!
• 2 + 8 = 10 (Southwest Xun 2 Fire + Northeast Zhen 8 Wood): “Thunder and Wind Arouse Each Other” (`Lei Feng Xiang Bo`). Again, 8 Wood produces 2 Fire!

Stop and look. Numbers lock together. Marvel at that mathematical miracle! Look at all four `He Shi` Sum-of-Ten pairs (`1–9, 4–6, 3–7, 2–8`): in every single Sum-of-Ten pair without exception, the two He Tu Five Phases are in a Productive Mother-Child relationship (`Metal produces Water` in `1–9` and `4–6`; `Wood produces Fire` in `3–7` and `2–8`)! Never once do two Sum-of-Ten partners clash or control each other! That is why `He Shi` (`A + B = 10`) is universally auspicious across Xuan Kong Da Gua.

5. Why Every 180° Sitting-Facing Axis Automatically Forms Gua Qi Sum-of-Ten

Let us prove a fundamental theorem of the 64-hexagram compass ring that every practitioner must know by heart: At any compass azimuth `θ`, the Sitting Hexagram at `θ` and the Facing Hexagram at `θ + 180°` ALWAYS sum to 10 in Gua Qi (`Q_sit + Q_face = 10`) AND ALWAYS share the exact same Star Period (`Yun_sit = Yun_face`)!

Why is this true at every single degree of the 360° circle? Because on Shao Yong’s Fu Xi 64-Hexagram Circle, any two hexagrams standing 180° apart across the center of the compass are Six-Line Structural Opposites (Cuo Gua 錯卦) where every Yin line (`0`) flips to Yang (`1`) and every Yang line (`1`) flips to Yin (`0`):

• Because all 3 lines of the Upper Trigram flip (`U_face = NOT(U_sit)`), the Upper Trigrams of Sitting and Facing are Early Heaven opposites (`Qian 9 ↔ Kun 1`, `Dui 4 ↔ Gen 6`, `Li 3 ↔ Kan 7`, `Zhen 8 ↔ Xun 2`), so their Gua Qi numbers always satisfy `Q_sit + Q_face = 10`!
• Because all 3 lines of the Lower Trigram ALSO flip (`L_face = NOT(L_sit)`), the bitwise XOR difference between Upper and Lower Trigrams remains 100% unchanged: NOT(U) ⊕ NOT(L) = U ⊕ L! Therefore, `Yun_sit == Yun_face` at every single degree on the compass!

Wait—if Sitting and Facing on a straight line automatically satisfy `Q_sit + Q_face = 10` and `Yun_sit = Yun_face`, why isn’t every house on Earth auspicious? Look at the two reasons: first, even though `Q_sit + Q_face = 10` is a productive relationship, direction matters—in half of all orientations (`Sitting 9 Metal facing 1 Water`, `Sitting 4 Metal facing 6 Water`, `Sitting 3 Wood facing 7 Fire`, `Sitting 8 Wood facing 2 Fire`), the Sitting Mountain is producing the Facing Direction (Sheng Chu 生出 — Outward Leakage) unless reversed by the Moving Line, the Inner Ring, or the Water Mouth! Second, a house is only auspicious when the external Incoming Dragon, Water Mouth, Door, Stove, and Date Selection Chart lock into resonance with that Sitting-Facing axis!

6. Law 4: Host-Guest Five-Phase Flow — Sheng Ru, Ke Ru, Sheng Chu & Ke Chu

This brings us to one of the most decisive operational rules in Xuan Kong Da Gua field auditing: Host-Guest Five-Phase Interaction (Zhu Bin Wu Xing Sheng Ke 主賓五行生剋).

In every pairing between two vectors, we first identify who is the Host (Zhu 主 / Wo 我 — “Me”) and who is the Guest (Bin 賓 / Ta 他 — “The Other”):

• Between Sitting Mountain and Facing / Water / Door / Date: The Sitting Mountain (and the Owner’s Birth Hexagram) is the Host (Me); the Facing Direction, Incoming Water, Main Door, Stove, and Date Selection Chart are the Guests coming toward the Host.

When we compare the He Tu Five Phase of the Guest (`1–6 Water, 2–7 Fire, 3–8 Wood, 4–9 Metal`) with the He Tu Five Phase of the Host, five interaction states arise:

7. Law 5: Gua Yun (Star Period) Pairings — Tong Yun, He Wu, He Shi & He Shi Wu

While Gua Qi governs the spatial Five-Phase Substance (Ti), Gua Yun (Star Period 1–9) governs the temporal Function (Yong). How must the Star Periods of the Dragon, Mountain, Facing, Water, and Date Chart relate to one another? Classical San Yuan lineages recognize four auspicious Star Period couplings:

1. Yi Yun Chun Qing (Same Star Period — Tong Yun 同運): All coupled hexagrams share the exact same Star Period (`e.g., Period 9 + Period 9`, or `Period 1 + Period 1`).
2. Gua Yun He Shi (Star Periods Sum to Ten — 卦運合十): The Star Periods of the coupled hexagrams sum to 10: `1 + 9 = 10`, `2 + 8 = 10`, `3 + 7 = 10`, `4 + 6 = 10`. In Period 9 (2024–2043), pairing a Period-9 Sitting Hexagram with a Period-1 Water Mouth or Date Chart (`9 + 1 = 10`) is the supreme Direct-Indirect Spirit formula!
3. Gua Yun He Wu & He Shi Wu (Star Periods Sum to 5 or 15 — 合五 · 合十五): Pairing Star Periods within the Lower Yuan (`1 + 4 = 5` or `2 + 3 = 5`) or Upper Yuan (`6 + 9 = 15` or `7 + 8 = 15`), mirroring the Central Palace 5 and the Luo Shu line sum of 15.
4. Gua Yun He Sheng Cheng (Star Periods Differ by 5 — `1–6, 2–7, 3–8, 4–9`): Connecting a hexagram’s Star Period with its He Tu partner (`|Yun_A − Yun_B| = 5`).

8. San Ban Fu Mu Gua (1-4-7, 2-5-8, 3-6-9) & Three-Cycle Invincibility

Why do ordinary buildings prosper for 20 years and then suffer sudden bankruptcy when the 20-year Period changes, whereas historic clan ancestral halls and dynastic estates built by San Yuan masters thrive across all 180 years (Three Cycles and Nine Periods — San Yuan Bu Bai 三元不敗)?

The secret is the San Ban Gua Triad Law (三般卦): linking the Upper Cycle (Periods 1, 2, 3), Middle Cycle (Periods 4, 5, 6), and Lower Cycle (Periods 7, 8, 9) through a constant step of `3`:

• First San Ban Triad (`1 – 4 – 7` — Meng / Eldest Triad): Bridges Period 1 (Upper Yuan) + Period 4 (Middle Yuan) + Period 7 (Lower Yuan).
• Second San Ban Triad (`2 – 5 – 8` — Zhong / Middle Triad): Bridges Period 2 (Upper Yuan) + Center 5 (Middle Yuan) + Period 8 (Lower Yuan).
• Third San Ban Triad (`3 – 6 – 9` — Ji / Youngest Triad): Bridges Period 3 (Upper Yuan) + Period 6 (Middle Yuan) + Period 9 (Lower Yuan).

When a site’s Dragon, Sitting, Facing, and Water Mouth (or internal courtyard water features) link all three numbers of a San Ban Triad—such as `1–4–7` or `3–6–9`—in either Gua Qi or Gua Yun, the property possesses an active antenna in the Upper, Middle, AND Lower Cycles simultaneously!

9. Qi Xing Da Jie (Seven-Star Robbery) in Xuan Kong Da Gua Architecture

Closely allied with the San Ban Triads is the famous Qi Xing Da Jie (七星打劫 — “Seven-Star Robbery of Future Qi”) recorded in the Tian Yu Jing. Why is it called “Seven-Star”? Because on the circle of 8 Trigram Palaces around the compass, counting 7 steps clockwise or counter-clockwise from any palace lands on the next member of its `1–4–7`, `2–5–8`, or `3–6–9` triad, while in the 64-hexagram matrix, pairing a Parent Hexagram (Period 1 Pure Gua or Period 9 Inverted Gua) at the Sitting/Facing axis with triad water mouths in the `1–4–7` or `3–6–9` palaces allows the building in Period 9 to “rob” and circulate the coming qi of Period 1 (2044–2063) and Period 3/6 ahead of time!

10. Master Evaluation Matrix: Grading Any Hexagram Pairing from S-Tier to Taboo

How do we combine all five laws when auditing a real building or selecting an auspicious construction date? Use the UK Master Academy Four-Vector Coupling Scorecard in Table 4.1 and Figure 4.4–4.5 below:

11. Field Case Study: Engineering a 1-6-1-6 Pure Water Industrial Park in Binh Duong

12. Frequently Asked Questions (FAQ) & Authoritative Classical Bibliography

1. What are the five main hexagram pairing rules in Xuan Kong Da Gua?

The five core pairing laws are: (1) Yi Gua Chun Qing (Pure One Qi — identical Gua Qi number across factors); (2) He Sheng Cheng (He Tu Generative Difference of Five: 1–6 Water, 2–7 Fire, 3–8 Wood, 4–9 Metal); (3) He Shi (Luo Shu Sum-of-Ten: 1+9, 2+8, 3+7, 4+6 = 10); (4) Host-Guest Five-Phase Inflow (Sheng Ru and Ke Ru); and (5) Gua Yun & San Ban Fu Mu Resonance (`1–4–7, 2–5–8, 3–6–9` triads and Period Sum-of-Ten).

2. In Host-Guest Five-Phase pairing, why is Ke Ru (Controlling Inflow) considered auspicious alongside Sheng Ru (Productive Inflow)?

In Xuan Kong Da Gua, the Sitting Mountain (or House Host) is the Master (Zhu) and the Facing Direction, Water Mouth, or Date Chart is the Guest (Bin). When Guest produces Host (Sheng Ru), external qi nourishes the family. When Guest controls a strong Host (Ke Ru), external wealth and authority press directly into the house’s embrace (“Ke Ru Jin Cai” — Controlling Inflow Brings Rapid Wealth). Conversely, Sheng Chu and Ke Chu drain the Host.

3. Why do every Sitting Hexagram and its 180-degree opposite Facing Hexagram automatically sum to 10 in Gua Qi?

Because every hexagram at θ° and its opposite at (θ + 180)° are 100% Yin-Yang opposites (Cuo Gua). Their Upper Trigrams are Early Heaven opposites (Qian 9 vs Kun 1, Dui 4 vs Gen 6, Li 3 vs Kan 7, Zhen 8 vs Xun 2), so their Gua Qi always sums to 10 (9+1, 4+6, 3+7, 8+2), while their Gua Yun Star Periods are 100% identical.

4. How do you pair Dragon with Water and Sitting Mountain with Facing Direction?

Classical San Yuan canons follow the Four-Node Coupling Law: Incoming Dragon pairs with Sitting Mountain (Yin with Yin), and Facing Direction pairs with Incoming/Gathering Water (Yang with Yang)—or all four nodes unite into a single Yi Gua Chun Qing or He Shi family.

Classical Sources & Academic References

1. Yang Yun Song (楊筠松, Tang Dynasty), Tian Yu Jing (天玉經) & Qing Nang Ao Yu (青囊奧語).
2. Jiang Dahong (蔣大鴻, Ming–Qing Transition), Di Li Bian Zheng (地理辨正) & Shui Long Jing (水龍經).
3. Zhang Zhong Shan (章仲山, Qing Dynasty), Di Li Bian Zheng Zai Bian (地理辨正再辨).
4. Zeng Zi Nan (曾子南, Taiwan San Yuan Lineage), Xuan Kong Da Gua Compendium.