> For the complete documentation index, see [llms.txt](https://alpaca4d.gitbook.io/docs/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://alpaca4d.gitbook.io/docs/basics/elements/four-node-tetrahedron.md).

# Four Node Tetrahedron

The **four node tetrahedron** is a linear 3D solid element. It is the fallback for volumetric geometry that will not mesh into hexahedra — which is most geometry that was not drawn with bricking in mind.

## 🔧 Grasshopper component

`FourNodeTetrahedron (Alpaca4d)` — **Alpaca4d ▸ 02\_Element**

Constructs one tetrahedral element from one 4-vertex mesh.

### Inputs

| Name     | Nick       | Type     | Default               | Description                                                                                           |
| -------- | ---------- | -------- | --------------------- | ----------------------------------------------------------------------------------------------------- |
| Mesh     | `Mesh`     | Mesh     | —                     | Tetrahedral mesh with **4 vertices**, in `m`. Passed through `CleanTetrahedron` to order the corners. |
| Material | `Material` | Material | —                     | An [nD material](/docs/basics/materials/nd.md).                                                       |
| Colour   | `Colour`   | Colour   | Alpaca4d brick colour | Display colour in the Rhino viewport.                                                                 |

### Outputs

| Name    | Nick      | Type    | Description                                                                   |
| ------- | --------- | ------- | ----------------------------------------------------------------------------- |
| Element | `Element` | Element | Tetrahedral element, to be connected to [Assemble](/docs/basics/assemble.md). |

## 📈 When to use it

**Use it when**

* The volume you need to model cannot be meshed into hexahedra.
* You are filling an irregular or free-form solid region.

**Do not use it when**

* A hexahedral mesh is available → prefer [SSP Brick](/docs/basics/elements/brick.md). The linear tetrahedron has a constant strain field, so it is stiff in bending and needs a much finer mesh to reach the same accuracy.
* The body is thin → use [Shell](/docs/basics/elements/shell.md).

## 🔗 Relation to OpenSees

```tcl
element FourNodeTetrahedron $eleTag $n1 $n2 $n3 $n4 $matTag $bx $by $bz
```

* The 4 mesh vertices map to `$n1 … $n4`.
* `$matTag` is the **Material** input.
* Body forces are not exposed by the component; use [Gravity Load](/docs/basics/loads/gravity.md) for self-weight.

Tetrahedron nodes have **3 DOF**.