> ## Documentation Index
> Fetch the complete documentation index at: https://docs.claviscage.app/llms.txt
> Use this file to discover all available pages before exploring further.

# Cage Types Reference

> Color-coded reference for all detected cage types

# Cage Types Reference

Clavis detects and color-codes hydrate cage polyhedra by their face signature. The available labels depend on the selected algorithm: TRACE accepts arbitrary signatures, HTR reports generalized `n4-n5-n6` counts, and GRADE is restricted to `5^12`, `5^12·6^2`, and `5^12·6^4`.

## Face Signature Notation

Cages are described by their polyhedral face composition. For example:

* **5^12** means 12 pentagonal faces (dodecahedron)
* **5^12·6^2** means 12 pentagons + 2 hexagons (tetrakaidecahedron)
* **4^1·5^10·6^2** means 1 square + 10 pentagons + 2 hexagons

## SEC Cage Types (Standard Edge-saturated Cages)

These are TRACE display types for complete cages satisfying the Euler relation F - E + V = 2. Their presence does not imply a GRADE structure verdict.

| Face Signature | Common Name        | Structure    | Color                                                        |
| -------------- | ------------------ | ------------ | ------------------------------------------------------------ |
| 5^12           | Dodecahedron       | sI/sII small | <span style={{color: '#06b6d4'}}>Cyan #06b6d4</span>         |
| 5^12·6^2       | Tetrakaidecahedron | sI large     | <span style={{color: '#8b5cf6'}}>Purple #8b5cf6</span>       |
| 5^12·6^3       | -                  | -            | <span style={{color: '#f59e0b'}}>Amber #f59e0b</span>        |
| 5^12·6^4       | Hexakaidecahedron  | sII large    | <span style={{color: '#ef4444'}}>Red #ef4444</span>          |
| 5^12·6^5       | -                  | -            | <span style={{color: '#22c55e'}}>Green #22c55e</span>        |
| 5^12·6^6       | -                  | -            | <span style={{color: '#ec4899'}}>Pink #ec4899</span>         |
| 5^12·6^8       | Icosahedron        | sH large     | <span style={{color: '#3b82f6'}}>Blue #3b82f6</span>         |
| 4^1·5^10·6^2   | -                  | -            | <span style={{color: '#14b8a6'}}>Teal #14b8a6</span>         |
| 4^1·5^10·6^3   | -                  | -            | <span style={{color: '#0ea5e9'}}>Sky #0ea5e9</span>          |
| 4^1·5^10·6^4   | -                  | -            | <span style={{color: '#6366f1'}}>Indigo #6366f1</span>       |
| 4^1·5^10·6^5   | -                  | -            | <span style={{color: '#a78bfa'}}>Violet #a78bfa</span>       |
| 4^2·5^8·6^1    | -                  | -            | <span style={{color: '#f97316'}}>Orange #f97316</span>       |
| 4^2·5^8·6^2    | -                  | -            | <span style={{color: '#fb923c'}}>Light Orange #fb923c</span> |
| 4^2·5^8·6^3    | -                  | -            | <span style={{color: '#d946ef'}}>Fuchsia #d946ef</span>      |
| 4^2·5^8·6^4    | -                  | -            | <span style={{color: '#f43f5e'}}>Rose #f43f5e</span>         |
| 4^3·5^6·6^3    | -                  | sH medium    | <span style={{color: '#84cc16'}}>Lime #84cc16</span>         |
| 4^3·5^6·6^4    | -                  | -            | <span style={{color: '#65a30d'}}>Dark Lime #65a30d</span>    |
| Other          | Unclassified       | -            | <span style={{color: '#9ca3af'}}>Gray #9ca3af</span>         |

## Incomplete Cages (IC)

Incomplete cages are partially formed structures missing some faces. They are rendered with pastel colors.

| Label       | Description                   | Color                                                            |
| ----------- | ----------------------------- | ---------------------------------------------------------------- |
| IC:5^12     | Incomplete dodecahedron       | <span style={{color: '#b0c4de'}}>Light Steel Blue #b0c4de</span> |
| IC:5^12·6^2 | Incomplete tetrakaidecahedron | <span style={{color: '#c9b8d1'}}>Lavender #c9b8d1</span>         |
| IC:5^12·6^4 | Incomplete hexakaidecahedron  | <span style={{color: '#b8d4c9'}}>Mint #b8d4c9</span>             |
| IC:unknown  | Unidentified incomplete cage  | <span style={{color: '#d4d4d4'}}>Light Gray #d4d4d4</span>       |

## Non-SEC Cages (nSEC)

Non-standard cages that form closed polyhedra but have unusual topology (e.g., odd ring sizes, non-planar faces).

| Label         | Description                     | Color                                                    |
| ------------- | ------------------------------- | -------------------------------------------------------- |
| nSEC:5^12     | Non-standard dodecahedron       | <span style={{color: '#87ceeb'}}>Sky Blue #87ceeb</span> |
| nSEC:5^12·6^2 | Non-standard tetrakaidecahedron | <span style={{color: '#dda0dd'}}>Plum #dda0dd</span>     |
| nSEC:5^12·6^4 | Non-standard hexakaidecahedron  | <span style={{color: '#98d8c8'}}>Aqua #98d8c8</span>     |
| nSEC:unknown  | Unidentified non-standard cage  | <span style={{color: '#c0c0c0'}}>Silver #c0c0c0</span>   |

## HTR Ring Types

When using the HTR algorithm, individual primitive rings are also visualized:

| Ring Type | Color                                                  |
| --------- | ------------------------------------------------------ |
| 4-ring    | <span style={{color: '#fbbf24'}}>Yellow #fbbf24</span> |
| 5-ring    | <span style={{color: '#06b6d4'}}>Cyan #06b6d4</span>   |
| 6-ring    | <span style={{color: '#a855f7'}}>Purple #a855f7</span> |

HTR cage counts use `n4-n5-n6`; for example, `0-12-0` corresponds to `5^12`. GRADE uses only the three canonical machine labels `512`, `51262`, and `51264`.

## Quality Levels

Each detected cage is assigned a quality level:

| Quality  | Code | Meaning                                                |
| -------- | ---- | ------------------------------------------------------ |
| **SEC**  | 2    | Standard edge-saturated cage with valid Euler topology |
| **nSEC** | 1    | Closed polyhedron with non-standard topology           |
| **IC**   | 0    | Incomplete cage, missing faces or edges                |