
## Polyhedra Provided by Number

There are fifteen polyhedra that can be created by setting their type number from 0 to 14. These are:

| type | name                                 | number of faces |
| ---- | ------------------------------------ | --------------- |
| 0    | Tetrahedron                          | 4               |
| 1    | Octahedron                           | 8               |
| 2    | Dodecahedron                         | 12              |
| 3    | Icosahedron                          | 20              |
| 4    | Rhombicuboctahedron                  | 26              |
| 5    | Triangular Prism                     | 5               |
| 6    | Pentagonal Prism                     | 7               |
| 7    | Hexagonal Prism                      | 8               |
| 8    | Square Pyramid (J1)                  | 5               |
| 9    | Pentagonal Pyramid (J2)              | 6               |
| 10   | Triangular Dipyramid (J12)           | 6               |
| 11   | Pentagonal Dipyramid (J13)           | 10              |
| 12   | Elongated Square Dipyramid (J15)     | 12              |
| 13   | Elongated Pentagonal Dipyramid (J16) | 15              |
| 14   | Elongated Pentagonal Cupola (J20)    | 22              |

## MeshBuilder

usage :

```javascript
const polyhedron = BABYLON.MeshBuilder.CreatePolyhedron("oct", options, scene); //scene is optional and defaults to the current scene
```

| option          | value                                                                                              | default value                    |
| --------------- | -------------------------------------------------------------------------------------------------- | -------------------------------- |
| type            | _(number)_ polyhedron type in the range [0,14]                                                     | 0                                |
| size            | _(number)_ polyhedron size                                                                         | 1                                |
| sizeX           | _(number)_ X polyhedron size, overwrites the _size_ property                                       | 1                                |
| sizeY           | _(number)_ Y polyhedron size, overwrites the _size_ property                                       | 1                                |
| sizeZ           | _(number)_ Z polyhedron size, overwrites the _size_ property                                       | 1                                |
| custom          | _(polygonObjectReference)_ a polyhedron object, overwrites the _type_ property                     | null                             |
| faceColors      | _(Color4[])_ array of _Color4_, one per face                                                       | Color4(1, 1, 1, 1) for each side |
| faceUV          | _(Vector4[])_ array of _Vector4_, one per face                                                     | UVs(0, 0, 1, 1) for each side    |
| flat            | _(boolean)_ if false, a polyhedron has a single global face, _faceUV_ and _faceColors_ are ignored | true                             |
| updatable       | _(boolean)_ true if the mesh is updatable                                                          | false                            |
| sideOrientation | _(number)_ side orientation                                                                        | DEFAULTSIDE                      |

To understand how to set _faceUV_ or _faceColors_, please read about [Face Colors and Textures for a Box](/features/featuresDeepDive/materials/using/texturePerBoxFace) taking into account the right number of faces of your polyhedron, instead of only 6 for a box.

## Examples

The full set of 15: <Playground id="#PBLS4Y" title="Full Set Of 15 Polyhedra" description="Playground example showing all 15 provided polyhedra."/>
Dodecahedron with FaceUVs: <Playground id="#PBLS4Y#1" title="Dodecahedron with FaceUVs" description="Playground example of creating a dodecahedron with faceUVs."/>

## Mesh

usage :

```javascript
const polyhedron = BABYLON.Mesh.CreatePolyhedron("oct", options, scene); //scene is optional and defaults to the current scene
```

This is the same format as that for _MeshBuilder_.



## Custom Polyhedra
This is another range of polyhedra that you can create, although they require a few more steps. This is the reason for the *custom* option. All the other options, other than *type*, can be used with custom polyhedra.

### From faces to triangles

In custom polyhedron data, `vertex` contains positions, and each entry in `face` lists indices into `vertex` around the perimeter of one face. List the corners in order, not as an unordered set: Babylon.js turns each face into triangles by using its first index as a shared corner. For a face with five corners:

```javascript
face: [[0, 1, 2, 3, 4]]
```

Babylon.js creates three triangles, with indices `(0, 2, 1)`, `(0, 3, 2)`, and `(0, 4, 3)`. In general, a face `[f0, f1, ..., fn]` becomes `(f0, f2, f1)`, `(f0, f3, f2)`, and so on through `(f0, fn, fn-1)`. The reversed order of the last two corners in each triangle is intentional.

The first corner also determines *which* diagonals are drawn. For example, `[1, 2, 3, 4, 0]` follows the same perimeter but produces `(1, 3, 2)`, `(1, 4, 3)`, and `(1, 0, 4)` instead. Both orders cover the same area if the face is flat and convex, but they produce different triangles; if its vertices are not coplanar, the resulting surface can look different. Reversing the perimeter order changes the triangle winding, which changes which side is the front and the direction of the computed normals. Keep the winding consistent across faces so their normals point outward. See [custom mesh normals and direction](/features/featuresDeepDive/mesh/creation/custom/custom#direction) for an illustrated explanation.

This first-corner triangle fan does not correctly triangulate every concave face. For a concave shape, split it into triangular `face` entries yourself rather than relying on the fan.


1.  Visit <Playground id="#WL3U6F" title="Custom Polyhedra" description="Simple example of custom polyhedra in Babylon.js."/> and minimize the code editor by unchecking the box labeled Editor under the Gear icon &#9881; (Options), then note the polyhedron names under the mouse pointer.  
![Select a Polyhedron](/img/how_to/Mesh/polyhedra1.webp);

2. From the polyhedra.js file at https://github.com/BabylonJS/Extensions/tree/master/Polyhedron, find the required name.
```javascript
HeptagonalPrism : {
"name":"Heptagonal Prism",
"category":["Prism"],
"vertex":[[0,0,1.090071],[0.796065,0,0.7446715],[-0.1498633,0.7818315,0.7446715],[-0.7396399,-0.2943675,0.7446715],[0.6462017,0.7818315,0.3992718],[1.049102,-0.2943675,-0.03143449],[-0.8895032,0.487464,0.3992718],[-0.8658909,-0.6614378,-0.03143449],[0.8992386,0.487464,-0.3768342],[0.5685687,-0.6614378,-0.6538232],[-1.015754,0.1203937,-0.3768342],[-0.2836832,-0.8247995,-0.6538232],[0.4187054,0.1203937,-0.9992228],[-0.4335465,-0.042968,-0.9992228]],
"face":[[0,1,4,2],[0,2,6,3],[1,5,8,4],[3,6,10,7],[5,9,12,8],[7,10,13,11],[9,11,13,12],[0,3,7,11,9,5,1],[2,4,8,12,13,10,6]]},
```

 
3. Copy and paste the desired polyhedron object into your code like this:

```javascript
const heptagonalPrism = { "name":"Heptagonal Prism", "category":["Prism"], "vertex":[[0,0,1.090071],[0.796065,0,0.7446715],[-0.1498633,0.7818315,0.7446715],[-0.7396399,-0.2943675,0.7446715],[0.6462017,0.7818315,0.3992718],[1.049102,-0.2943675,-0.03143449],[-0.8895032,0.487464,0.3992718],[-0.8658909,-0.6614378,-0.03143449],[0.8992386,0.487464,-0.3768342],[0.5685687,-0.6614378,-0.6538232],[-1.015754,0.1203937,-0.3768342],[-0.2836832,-0.8247995,-0.6538232],[0.4187054,0.1203937,-0.9992228],[-0.4335465,-0.042968,-0.9992228]],
"face":[[0,1,4,2],[0,2,6,3],[1,5,8,4],[3,6,10,7],[5,9,12,8],[7,10,13,11],[9,11,13,12],[0,3,7,11,9,5,1],[2,4,8,12,13,10,6]]};

const heptPrism = BABYLON.MeshBuilder.CreatePolyhedron("h", {custom: heptagonalPrism}, scene); //scene is optional and defaults to the current scene

//also possible
const heptPrism1 = BABYLON.Mesh.CreatePolyhedron("h", {custom: heptagonalPrism}, scene); //scene is optional and defaults to the current scene
```
 &nbsp;
 &nbsp;   
HeptagonalPrism: <Playground id="#PBLS4Y#2" title="HeptagonalPrism" description="Simple example of a heptagonalPrism."/>
Heptagonal Prism with changed sizes: <Playground id="#PBLS4Y#3" title="HeptagonalPrism With Changed Sizes" description="Simple example of a heptagonalPrism with changed sizes."/>
Heptagonal Prism with face colors: <Playground id="#PBLS4Y#4" title="HeptagonalPrism With Face Colors" description="Simple example of a heptagonalPrism with face colors."/>


## Polyhedra
There are many polyhedra, too many for each to be created under its own name. Their names are often long anyway, so Babylon.js provides 15 common ones by number. There are many beyond these 15, and those can be created from custom data sets provided in the form of Playground examples. 

The twenty-sided icosahedron has the interesting property of approximating a sphere. By dividing each face into triangles and then mapping the resulting vertices onto a sphere, it gives a better approximation of a sphere. The solids formed are called icospheres and provide a more regular distribution of triangles around a sphere than the *CreateSphere* method.

Other sphere approximations can be provided by geodesic and Goldberg polyhedra. Like the icosphere, a geodesic polyhedron is based on an icosahedron and formed from equilateral triangles. In this case, however, their arrangement depends on two integer parameters, m and n. A Goldberg polyhedron is the dual of a geodesic one, and vice versa. A dual polyhedron is formed by mapping its vertices to the faces of the dual and its faces to the dual's vertices. A Goldberg polyhedron is made up of 12 pentagonal faces and many hexagonal faces, and has the advantage of providing a planet-shaped hexagon-grid world.

![Geodesic Vertices](/img/snippets/geo30.webp)  
The arrangement of vertices for a Geodesic Poly with m = 6 and n = 0, 1, 2 in order

type	name	number of faces
0	Tetrahedron	4
1	Octahedron	8
2	Dodecahedron	12
3	Icosahedron	20
4	Rhombicuboctahedron	26
5	Triangular Prism	5
6	Pentagonal Prism	7
7	Hexagonal Prism	8
8	Square Pyramid (J1)	5
9	Pentagonal Pyramid (J2)	6
10	Triangular Dipyramid (J12)	6
11	Pentagonal Dipyramid (J13)	10
12	Elongated Square Dipyramid (J15)	12
13	Elongated Pentagonal Dipyramid (J16)	15
14	Elongated Pentagonal Cupola (J20)	22

option	value	default value
type	(number) polyhedron type in the range [0,14]	0
size	(number) polyhedron size	1
sizeX	(number) X polyhedron size, overwrites the size property	1
sizeY	(number) Y polyhedron size, overwrites the size property	1
sizeZ	(number) Z polyhedron size, overwrites the size property	1
custom	(polygonObjectReference) a polyhedron object, overwrites the type property	null
faceColors	(Color4[]) array of Color4, one per face	Color4(1, 1, 1, 1) for each side
faceUV	(Vector4[]) array of Vector4, one per face	UVs(0, 0, 1, 1) for each side
flat	(boolean) if false, a polyhedron has a single global face, faceUV and faceColors are ignored	true
updatable	(boolean) true if the mesh is updatable	false
sideOrientation	(number) side orientation	DEFAULTSIDE

Provided Polyhedra

Polyhedra Provided by Number

MeshBuilder

Examples

Mesh