1 | initial version |

I do not know the details, but it is pretty easy to apply the matrix to all the vertices of the polyhedron.

2 | No.2 Revision |

I do not know the details, but it is pretty easy to apply the matrix to all the vertices of the polyhedron.

Regarding your second question, D is already a subset of some 3d space :

```
sage: D.ambient_space()
Vector space of dimension 3 over Number Field in sqrt5 with defining polynomial x^2 - 5 with sqrt5 = 2.236067977499790?
```

3 | No.3 Revision |

~~I do ~~Regarding your first question, Sage relies on various libraries to represent and deal with polyhedras, so there are various corresponding backends, like `ppl`

, `cdd`

, `normaliz`

, `polymake`

. In the case of your docahedron, the backend is named `field`

, which means that it relies on Sage own code, not ~~know ~~external library:

```
sage: D.backend()
'field'
```

Now, to see the ~~details, but it ~~corresponding source code, you can do:

```
sage: from sage.geometry.polyhedron.backend_field import Polyhedron_field
sage: Polyhedron_field??
```

As you can see, the internal representation of your polyhedron is ~~pretty easy to apply ~~both the ~~matrix to all ~~V-reprentation and the ~~vertices of the polyhedron.~~H-representation.

Regarding your second question, D is already a subset of some 3d space :

```
sage: D.ambient_space()
Vector space of dimension 3 over Number Field in sqrt5 with defining polynomial x^2 - 5 with sqrt5 = 2.236067977499790?
```

4 | No.4 Revision |

Regarding your first question, Sage relies on various libraries to represent and deal with polyhedras, so there are various corresponding backends, like `ppl`

, `cdd`

, `normaliz`

, `polymake`

. In the case of your docahedron, the backend is named `field`

, which means that it relies on Sage own code, not external library:

```
sage: D.backend()
'field'
```

Now, to see the corresponding source code, you can do:

```
sage: from sage.geometry.polyhedron.backend_field import Polyhedron_field
sage: Polyhedron_field??
```

As you can see, the internal representation of your polyhedron is both the V-reprentation and the ~~H-representation.~~H-representation. In both cases, it is pretty easy so see how a matrix acts on them.

Regarding your second question, D is already a subset of some 3d space :

```
sage: D.ambient_space()
Vector space of dimension 3 over Number Field in sqrt5 with defining polynomial x^2 - 5 with sqrt5 = 2.236067977499790?
```

5 | No.5 Revision |

Regarding your first question, Sage relies on various libraries to represent and deal with polyhedras, so there are various corresponding backends, like `ppl`

, `cdd`

, `normaliz`

, `polymake`

. In the case of your docahedron, the backend is named `field`

, which means that it relies on Sage own code, not external library:

```
sage: D.backend()
'field'
```

Now, to see the corresponding source code, you can do:

```
sage: from sage.geometry.polyhedron.backend_field import Polyhedron_field
sage: Polyhedron_field??
```

As you can see, the internal representation of your polyhedron is both the V-reprentation and the ~~H-representation. ~~H-representation, simultaneously. In both cases, it is pretty easy so see how a matrix acts on them.

Regarding your second question, D is already a subset of some 3d space :

```
sage: D.ambient_space()
Vector space of dimension 3 over Number Field in sqrt5 with defining polynomial x^2 - 5 with sqrt5 = 2.236067977499790?
```

Copyright Sage, 2010. Some rights reserved under creative commons license. Content on this site is licensed under a Creative Commons Attribution Share Alike 3.0 license.