TIANTAI · FOUR TEACHINGS

Buddhist Paths of Practice

Follow the six identities through the four teachings.

Identity expresses equality in principle; six distinguishes depth of realization. Begin with five illustrated guides, explore the six identities and four paths, and finish with the comprehensive reference chart.

01 / ILLUSTRATED STUDY

Illustrated guide to the six identities

Five illustrations · click any to enlarge
ILLUSTRATION / 01

Overview of the six identities

From principle to realization

Tiantai illustrated guide

Begin with the six identities. Cross-teaching matches in the artwork are approximate; use the comparison above for the distinctions.

English reading guide to the Chinese artwork

Read the six levels from bottom to top: principle, name, practice, resemblance, partial realization and ultimate realization. The comparisons below the tower are approximate, rather than exact equivalents across the four teachings.

Begin with the six identities. Cross-teaching matches in the artwork are approximate; use the comparison above for the distinctions.

理即佛 · Identity in principle
Inherent principle, before understanding

In the Perfect teaching, all beings possess the inconceivable principle. “Identity” expresses nonduality; “six” distinguishes depth of practice. Inherent Buddha nature is not completed realization.

名字即佛 · Identity in name
Understanding through the teaching

One hears and understands the teaching of the middle. Knowing terminology alone does not establish direct realization.

观行即佛 · Identity in practice
Five grades · outer ordinary stage

The five grades are rejoicing, reading and reciting, explaining, additionally practicing the six perfections, and making them the principal practice. Afflictions are subdued; other teachings provide approximate comparisons.

相似即佛 · Identity in resemblance
Ten faiths · inner ordinary stage

The ten faiths purify the six faculties. They progressively remove errors of view, thought and knowledge, while subduing ignorance. Partial realization of the Dharma body has yet to begin.

分证即佛 · Identity in partial realization
First abode through equal awakening · 41 stages

At the first abode, a portion of ignorance is removed and the Dharma body is partially realized. The ten abodes, practices, dedications and grounds, plus equal awakening, form 41 stages. Distinct teaching realization begins at the first ground; identical stage names are not equivalent.

究竟即佛 · Identity in ultimate realization
Perfect teaching: wondrous awakening

Wondrous awakening in the Perfect teaching is ultimate realization. A shared destination illustrates convergence into the Perfect Buddha vehicle. Within the separate doctrinal systems, Distinct wondrous awakening corresponds only to a partial realization stage in the Perfect teaching.

Explain terms in this illustration

Identity in principle:In the Perfect teaching, all beings possess the inconceivable principle. “Identity” expresses nonduality; “six” distinguishes depth of practice. Inherent Buddha nature is not completed realization.

Identity in name:One hears and understands the teaching of the middle. Knowing terminology alone does not establish direct realization.

Identity in practice:The five grades are rejoicing, reading and reciting, explaining, additionally practicing the six perfections, and making them the principal practice. Afflictions are subdued; other teachings provide approximate comparisons.

Identity in resemblance:The ten faiths purify the six faculties. They progressively remove errors of view, thought and knowledge, while subduing ignorance. Partial realization of the Dharma body has yet to begin.

Identity in partial realization:At the first abode, a portion of ignorance is removed and the Dharma body is partially realized. The ten abodes, practices, dedications and grounds, plus equal awakening, form 41 stages. Distinct teaching realization begins at the first ground; identical stage names are not equivalent.

Identity in ultimate realization:Wondrous awakening in the Perfect teaching is ultimate realization. A shared destination illustrates convergence into the Perfect Buddha vehicle. Within the separate doctrinal systems, Distinct wondrous awakening corresponds only to a partial realization stage in the Perfect teaching.

ILLUSTRATION / 02

Principle · name · practice

From inherent nature to practice

Tiantai illustrated guide

The first three identities move from principle through understanding into practice. Perfect five grades can be compared with Distinct ten faiths, while their doctrines and contemplations differ.

English reading guide to the Chinese artwork

Read left to right: inherent Buddha nature, understanding through hearing the teaching, and putting that understanding into practice. The five grades belong to the Perfect teaching; Distinct ten faiths provide a comparison of depth, rather than an identical practice.

The first three identities move from principle through understanding into practice. Perfect five grades can be compared with Distinct ten faiths, while their doctrines and contemplations differ.

理即佛 · Identity in principle
Inherent principle, before understanding

In the Perfect teaching, all beings possess the inconceivable principle. “Identity” expresses nonduality; “six” distinguishes depth of practice. Inherent Buddha nature is not completed realization.

名字即佛 · Identity in name
Understanding through the teaching

One hears and understands the teaching of the middle. Knowing terminology alone does not establish direct realization.

观行即佛 · Identity in practice
Five grades · outer ordinary stage

The five grades are rejoicing, reading and reciting, explaining, additionally practicing the six perfections, and making them the principal practice. Afflictions are subdued; other teachings provide approximate comparisons.

Explain terms in this illustration

Identity in principle:In the Perfect teaching, all beings possess the inconceivable principle. “Identity” expresses nonduality; “six” distinguishes depth of practice. Inherent Buddha nature is not completed realization.

Identity in name:One hears and understands the teaching of the middle. Knowing terminology alone does not establish direct realization.

Identity in practice:The five grades are rejoicing, reading and reciting, explaining, additionally practicing the six perfections, and making them the principal practice. Afflictions are subdued; other teachings provide approximate comparisons.

ILLUSTRATION / 03

Identity in resemblance

Deep practice resembling truth

Tiantai illustrated guide

Compare Perfect ten faiths and Distinct preparatory stages by afflictions removed. The artwork’s “lesser vehicle” label is shorthand: both Tripiṭaka and Shared teachings include bodhisattvas.

English reading guide to the Chinese artwork

The three lower panels refer to Perfect ten faiths, the Distinct three groups of worthy stages (ten abodes, ten practices and ten dedications), and the artwork’s shorthand “lesser vehicle” label. These are comparisons of depth. Both Tripiṭaka and Shared teachings also include bodhisattvas.

Compare Perfect ten faiths and Distinct preparatory stages by afflictions removed. The artwork’s “lesser vehicle” label is shorthand: both Tripiṭaka and Shared teachings include bodhisattvas.

相似即佛 · Identity in resemblance
Ten faiths · inner ordinary stage

The ten faiths purify the six faculties. They progressively remove errors of view, thought and knowledge, while subduing ignorance. Partial realization of the Dharma body has yet to begin.

Explain terms in this illustration

Identity in resemblance:The ten faiths purify the six faculties. They progressively remove errors of view, thought and knowledge, while subduing ignorance. Partial realization of the Dharma body has yet to begin.

ILLUSTRATION / 04

Identity in partial realization

Break ignorance, partially realize the Dharma body

Tiantai illustrated guide

Partial realization begins at the first Perfect abode and first Distinct ground. The same names for subsequent groups do not make all stages equivalent.

English reading guide to the Chinese artwork

The left panel begins with the first Distinct ground; the right begins with the first Perfect abode. On the right, read the sequence: first abode → ten abodes → ten practices → ten dedications → ten grounds → equal awakening. Identically named stages in the two teachings cannot all be aligned directly.

Partial realization begins at the first Perfect abode and first Distinct ground. The same names for subsequent groups do not make all stages equivalent.

分证即佛 · Identity in partial realization
First abode through equal awakening · 41 stages

At the first abode, a portion of ignorance is removed and the Dharma body is partially realized. The ten abodes, practices, dedications and grounds, plus equal awakening, form 41 stages. Distinct teaching realization begins at the first ground; identical stage names are not equivalent.

Explain terms in this illustration

Identity in partial realization:At the first abode, a portion of ignorance is removed and the Dharma body is partially realized. The ten abodes, practices, dedications and grounds, plus equal awakening, form 41 stages. Distinct teaching realization begins at the first ground; identical stage names are not equivalent.

ILLUSTRATION / 05

Identity in ultimate realization

Convergence: distinguish doctrine from realization

Tiantai illustrated guide

The common destination illustrates convergence. In the doctrinal comparison of the Outline, Distinct wondrous awakening corresponds to the second Perfect practice, within partial realization. Ultimate unity is expressed through convergence into the Perfect teaching.

English reading guide to the Chinese artwork

The two stairways depict sequential practice in the Distinct teaching and integrated practice in the Perfect teaching. Their shared destination represents convergence into the Buddha vehicle. In doctrinal comparison, Distinct wondrous awakening corresponds to the second Perfect practice, within partial realization; it is not directly identical to Perfect ultimate realization.

The common destination illustrates convergence. In the doctrinal comparison of the Outline, Distinct wondrous awakening corresponds to the second Perfect practice, within partial realization. Ultimate unity is expressed through convergence into the Perfect teaching.

分证即佛 · Identity in partial realization
First abode through equal awakening · 41 stages

At the first abode, a portion of ignorance is removed and the Dharma body is partially realized. The ten abodes, practices, dedications and grounds, plus equal awakening, form 41 stages. Distinct teaching realization begins at the first ground; identical stage names are not equivalent.

究竟即佛 · Identity in ultimate realization
Perfect teaching: wondrous awakening

Wondrous awakening in the Perfect teaching is ultimate realization. A shared destination illustrates convergence into the Perfect Buddha vehicle. Within the separate doctrinal systems, Distinct wondrous awakening corresponds only to a partial realization stage in the Perfect teaching.

Explain terms in this illustration

Identity in partial realization:At the first abode, a portion of ignorance is removed and the Dharma body is partially realized. The ten abodes, practices, dedications and grounds, plus equal awakening, form 41 stages. Distinct teaching realization begins at the first ground; identical stage names are not equivalent.

Identity in ultimate realization:Wondrous awakening in the Perfect teaching is ultimate realization. A shared destination illustrates convergence into the Perfect Buddha vehicle. Within the separate doctrinal systems, Distinct wondrous awakening corresponds only to a partial realization stage in the Perfect teaching.

02 / FROM PRINCIPLE TO REALIZATION

The six identities

Choose a stage to read more
PERFECT TEACHING AXIS

Identity in principle

Inherent principle, before understanding

In the Perfect teaching, all beings possess the inconceivable principle. “Identity” expresses nonduality; “six” distinguishes depth of practice. Inherent Buddha nature is not completed realization.

03 / FOUR PATHS OF PRACTICE

Stages of the four teachings

Tripiṭaka

Analytical contemplation of emptiness · Four Noble Truths as arising and perishing

Primarily teaches śrāvakas and pratyekabuddhas; also describes the bodhisattva path through the six perfections.

Shared

Contemplation of inherent emptiness · Four Noble Truths as nonarising

A shared path for three vehicles. Phenomena are illusory and empty; receptive practitioners may be received into the Distinct or Perfect teaching.

Distinct

Sequential contemplation: empty, provisional, middle · Four Noble Truths as immeasurable

A bodhisattva path of sequential contemplation. Direct realization of the middle begins at the first ground.

Perfect

Threefold contemplation in one mind · Four Noble Truths as spontaneous

Empty, provisional and middle are inseparable. The six identities distinguish stages; partial realization begins at the first abode.

Read each teaching vertically. Identical identity names do not imply equal realization. Partial realization in the first two teachings is not Perfect realization of the Dharma body.

Six identities and the four paths
IdentityTripiṭakaAnalytical contemplation of emptiness · Four Noble Truths as arising and perishingSharedContemplation of inherent emptiness · Four Noble Truths as nonarisingDistinctSequential contemplation: empty, provisional, middle · Four Noble Truths as immeasurablePerfectThreefold contemplation in one mind · Four Noble Truths as spontaneous
One-sided truth

Truth approached through cessation

Non-arising

Phenomena do not inherently arise

Exclusive middle

The middle beyond the two extremes

Inconceivable principle

Mind, Buddha and beings are nondual

Understand dependent arising

Impermanence and no self

Understand illusory phenomena

Empty as they are, not through destruction

Trust in the middle

Understand and trust the nature of suchness

Understand the perfect middle

The middle in every phenomenon

Outer preparatory stages

Five calming methods → particular → comprehensive mindfulness

1 · Dry wisdom

Outer ordinary stage of the three vehicles

Ten faiths

Outer stage; subdues view and thought afflictions

Five grades

Rejoicing → recitation → explanation → additional → principal practice of the perfections

Four inner preparatory stages

Warmth → summit → acceptance → highest worldly stage

2 · Nature stage

Inner ordinary stage; subdues afflictions

Three groups · thirty stages

Ten abodes → ten practices → ten dedications

Ten faiths

View → thought → knowledge afflictions; ignorance subdued

First three fruits · training

Stream-enterer → once-returner → non-returner

Stages 3–9

Eight-person → seeing → attenuation → desire-free → accomplished → pratyekabuddha → bodhisattva

Ten grounds → equal awakening

Ignorance is broken from the first ground

41 stages of partial realization

Ten abodes → practices → dedications → grounds → equal awakening

Completion in the three vehicles

Arhat, pratyekabuddha, or Tripiṭaka Buddha; residual habits differ

10 · Buddha stage

Residual habits removed; completion within this teaching

Distinct wondrous awakening

Doctrinal completion; not Perfect ultimate realization

Wondrous awakening

All 42 portions of ignorance removed

Tripiṭaka

One-sided truth

Truth approached through cessation

Shared

Non-arising

Phenomena do not inherently arise

Distinct

Exclusive middle

The middle beyond the two extremes

Perfect

Inconceivable principle

Mind, Buddha and beings are nondual

Expand stage names and afflictions

Ten faiths: faith, mindfulness, effort, wisdom, concentration, non-retrogression, dedication, protecting Dharma, discipline, aspiration.

Ten abodes: aspiration, preparation, practice, noble birth, skillful means, right mind, non-retrogression, youthful purity, Dharma prince, consecration.

Ten practices: joy, benefit, freedom from anger, inexhaustibility, freedom from confusion, manifestation of good, non-attachment, respect, wholesome Dharma, truth.

Ten dedications: saving beings without attachment, indestructibility, equality with Buddhas, reaching all places, inexhaustible merit, equal roots of good, equal regard for beings, suchness, unbound liberation, immeasurable Dharma realm.

Ten grounds: joy, purity, radiance, blazing wisdom, difficult to conquer, presence, far-reaching, immovability, good wisdom, Dharma cloud.

Three kinds of affliction: errors of view and thought; obstacles to knowing the countless ways of helping beings; fundamental ignorance of the middle. Their removal must be understood within each teaching.

Tripiṭaka: three preliminary and four preparatory stages make seven worthy stages; the four śrāvaka fruits end in arhatship. The ten Shared stages are distinct from the bodhisattva ten grounds of the other teachings.

Expand the full paths and three-vehicle branches

Tripiṭaka

Śrāvaka: five calming methods → particular and comprehensive mindfulness → warmth → summit → acceptance → highest worldly stage (seven preparatory stages) → stream-entry → once-returning → non-returning → arhatship. Pratyekabuddha: contemplation of the twelve links → awakening, also weakening residual habits. Bodhisattva: vows and six perfections through three incalculable eons → a hundred eons cultivating marks → final birth → acceptance and highest worldly stage → thirty-four moments removing afflictions and habits → Tripiṭaka Buddhahood.

Shared

Ten shared stages: 1 dry wisdom → 2 nature → 3 eight-person → 4 seeing → 5 attenuation → 6 desire-free → 7 accomplished → 8 pratyekabuddha → 9 bodhisattva → 10 Buddha. Śrāvakas finish at stage 7 and pratyekabuddhas at 8. Bodhisattvas remain active for beings at 9 and remove remaining habits at 10. Reception into the Distinct or Perfect path is considered separately.

Distinct

Ten faiths → ten abodes (enter emptiness) → ten practices (enter the provisional) → ten dedications (practice the middle) → ten grounds (break ignorance from the first) → equal awakening → Distinct wondrous awakening. The system has 52 doctrinal stages. In comparison of realization: first ground ≈ first Perfect abode; tenth ground ≈ tenth abode; equal awakening ≈ first Perfect practice; wondrous awakening ≈ second practice.

Perfect

Principle → name → five grades (practice) → ten faiths (resemblance) → ten abodes → ten practices → ten dedications → ten grounds → equal awakening (41 stages of partial realization from the first abode) → wondrous awakening (ultimate). Partial removal of ignorance and realization of the Dharma body start at the first abode. The contemplation remains threefold in one mind throughout.

04 / COMPREHENSIVE REFERENCE

Traditional comprehensive chart

ILLUSTRATION / 06

Traditional comprehensive reference

Study reference · read with the text comparison

Tiantai illustrated guide

The supplied comprehensive chart is preserved for study. It contains design notes and simplified comparisons. Read it alongside both textual views above rather than as a precise doctrinal equivalence table.

English reading guide to the Chinese artwork

Read columns as the six identities and rows as Perfect, Distinct, Shared and Tripiṭaka teachings. The source artwork contains simplified comparisons and an editorial note about Excel; it is a study illustration. Use the textual table below to distinguish each teaching’s own stages. The journey symbols at the bottom refer to the conjured city and treasure destination in the Lotus Sutra; they are illustrations, not a scale of equivalent attainment.

The supplied comprehensive chart is preserved for study. It contains design notes and simplified comparisons. Read it alongside both textual views above rather than as a precise doctrinal equivalence table.

理即佛 · Identity in principle
Inherent principle, before understanding

In the Perfect teaching, all beings possess the inconceivable principle. “Identity” expresses nonduality; “six” distinguishes depth of practice. Inherent Buddha nature is not completed realization.

名字即佛 · Identity in name
Understanding through the teaching

One hears and understands the teaching of the middle. Knowing terminology alone does not establish direct realization.

观行即佛 · Identity in practice
Five grades · outer ordinary stage

The five grades are rejoicing, reading and reciting, explaining, additionally practicing the six perfections, and making them the principal practice. Afflictions are subdued; other teachings provide approximate comparisons.

相似即佛 · Identity in resemblance
Ten faiths · inner ordinary stage

The ten faiths purify the six faculties. They progressively remove errors of view, thought and knowledge, while subduing ignorance. Partial realization of the Dharma body has yet to begin.

分证即佛 · Identity in partial realization
First abode through equal awakening · 41 stages

At the first abode, a portion of ignorance is removed and the Dharma body is partially realized. The ten abodes, practices, dedications and grounds, plus equal awakening, form 41 stages. Distinct teaching realization begins at the first ground; identical stage names are not equivalent.

究竟即佛 · Identity in ultimate realization
Perfect teaching: wondrous awakening

Wondrous awakening in the Perfect teaching is ultimate realization. A shared destination illustrates convergence into the Perfect Buddha vehicle. Within the separate doctrinal systems, Distinct wondrous awakening corresponds only to a partial realization stage in the Perfect teaching.

Each teaching’s own stages: English text comparison
Identity藏教 · Tripiṭaka

Analytical contemplation of emptiness · Four Noble Truths as arising and perishing

通教 · Shared

Contemplation of inherent emptiness · Four Noble Truths as nonarising

别教 · Distinct

Sequential contemplation: empty, provisional, middle · Four Noble Truths as immeasurable

圆教 · Perfect

Threefold contemplation in one mind · Four Noble Truths as spontaneous

Identity in principleOne-sided truth

Truth approached through cessation

Non-arising

Phenomena do not inherently arise

Exclusive middle

The middle beyond the two extremes

Inconceivable principle

Mind, Buddha and beings are nondual

Identity in nameUnderstand dependent arising

Impermanence and no self

Understand illusory phenomena

Empty as they are, not through destruction

Trust in the middle

Understand and trust the nature of suchness

Understand the perfect middle

The middle in every phenomenon

Identity in practiceOuter preparatory stages

Five calming methods → particular → comprehensive mindfulness

1 · Dry wisdom

Outer ordinary stage of the three vehicles

Ten faiths

Outer stage; subdues view and thought afflictions

Five grades

Rejoicing → recitation → explanation → additional → principal practice of the perfections

Identity in resemblanceFour inner preparatory stages

Warmth → summit → acceptance → highest worldly stage

2 · Nature stage

Inner ordinary stage; subdues afflictions

Three groups · thirty stages

Ten abodes → ten practices → ten dedications

Ten faiths

View → thought → knowledge afflictions; ignorance subdued

Identity in partial realizationFirst three fruits · training

Stream-enterer → once-returner → non-returner

Stages 3–9

Eight-person → seeing → attenuation → desire-free → accomplished → pratyekabuddha → bodhisattva

Ten grounds → equal awakening

Ignorance is broken from the first ground

41 stages of partial realization

Ten abodes → practices → dedications → grounds → equal awakening

Identity in ultimate realizationCompletion in the three vehicles

Arhat, pratyekabuddha, or Tripiṭaka Buddha; residual habits differ

10 · Buddha stage

Residual habits removed; completion within this teaching

Distinct wondrous awakening

Doctrinal completion; not Perfect ultimate realization

Wondrous awakening

All 42 portions of ignorance removed

Stage groups and complete paths

Ten faiths: faith, mindfulness, effort, wisdom, concentration, non-retrogression, dedication, protecting Dharma, discipline, aspiration.

Ten abodes: aspiration, preparation, practice, noble birth, skillful means, right mind, non-retrogression, youthful purity, Dharma prince, consecration.

Ten practices: joy, benefit, freedom from anger, inexhaustibility, freedom from confusion, manifestation of good, non-attachment, respect, wholesome Dharma, truth.

Ten dedications: saving beings without attachment, indestructibility, equality with Buddhas, reaching all places, inexhaustible merit, equal roots of good, equal regard for beings, suchness, unbound liberation, immeasurable Dharma realm.

Ten grounds: joy, purity, radiance, blazing wisdom, difficult to conquer, presence, far-reaching, immovability, good wisdom, Dharma cloud.

Three kinds of affliction: errors of view and thought; obstacles to knowing the countless ways of helping beings; fundamental ignorance of the middle. Their removal must be understood within each teaching.

Tripiṭaka

Śrāvaka: five calming methods → particular and comprehensive mindfulness → warmth → summit → acceptance → highest worldly stage (seven preparatory stages) → stream-entry → once-returning → non-returning → arhatship. Pratyekabuddha: contemplation of the twelve links → awakening, also weakening residual habits. Bodhisattva: vows and six perfections through three incalculable eons → a hundred eons cultivating marks → final birth → acceptance and highest worldly stage → thirty-four moments removing afflictions and habits → Tripiṭaka Buddhahood.

Shared

Ten shared stages: 1 dry wisdom → 2 nature → 3 eight-person → 4 seeing → 5 attenuation → 6 desire-free → 7 accomplished → 8 pratyekabuddha → 9 bodhisattva → 10 Buddha. Śrāvakas finish at stage 7 and pratyekabuddhas at 8. Bodhisattvas remain active for beings at 9 and remove remaining habits at 10. Reception into the Distinct or Perfect path is considered separately.

Distinct

Ten faiths → ten abodes (enter emptiness) → ten practices (enter the provisional) → ten dedications (practice the middle) → ten grounds (break ignorance from the first) → equal awakening → Distinct wondrous awakening. The system has 52 doctrinal stages. In comparison of realization: first ground ≈ first Perfect abode; tenth ground ≈ tenth abode; equal awakening ≈ first Perfect practice; wondrous awakening ≈ second practice.

Perfect

Principle → name → five grades (practice) → ten faiths (resemblance) → ten abodes → ten practices → ten dedications → ten grounds → equal awakening (41 stages of partial realization from the first abode) → wondrous awakening (ultimate). Partial removal of ignorance and realization of the Dharma body start at the first abode. The contemplation remains threefold in one mind throughout.

Explain terms in this illustration

Identity in principle:In the Perfect teaching, all beings possess the inconceivable principle. “Identity” expresses nonduality; “six” distinguishes depth of practice. Inherent Buddha nature is not completed realization.

Identity in name:One hears and understands the teaching of the middle. Knowing terminology alone does not establish direct realization.

Identity in practice:The five grades are rejoicing, reading and reciting, explaining, additionally practicing the six perfections, and making them the principal practice. Afflictions are subdued; other teachings provide approximate comparisons.

Identity in resemblance:The ten faiths purify the six faculties. They progressively remove errors of view, thought and knowledge, while subduing ignorance. Partial realization of the Dharma body has yet to begin.

Identity in partial realization:At the first abode, a portion of ignorance is removed and the Dharma body is partially realized. The ten abodes, practices, dedications and grounds, plus equal awakening, form 41 stages. Distinct teaching realization begins at the first ground; identical stage names are not equivalent.

Identity in ultimate realization:Wondrous awakening in the Perfect teaching is ultimate realization. A shared destination illustrates convergence into the Perfect Buddha vehicle. Within the separate doctrinal systems, Distinct wondrous awakening corresponds only to a partial realization stage in the Perfect teaching.

Sources and further reading

Based on the supplied final presentation plan and six illustrations, with textual comparisons checked against the works below. Read the artwork as a guide alongside the doctrinal distinctions.

Outline of Teaching and Contemplation · four teachings and six identities ↗Outline of the Tiantai Fourfold Teachings · stages of practice ↗← Return to the Patriarchs’ Hall

Overview of the six identities

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Overview of the six identities