# Is there a function to map faces of a cone its dual?

Suppose `C`

is a full dimensional pointed rational polyhedral cone with vertex at the origin. Then there is a correspondence between faces of `C`

and faces of `C.dual()`

given by

```
F -> Fd := { y in C.dual() | <y, x> = 0 for all x in F }
```

This correspondence satisfies

```
dim(F)+dim(Fd)=dim(C)
```

I want to define the function (or dictionary) in sage that maps each face in `C.face_lattice()`

to its corresponding face in `C.dual().face_lattice()`

. Does this function exist in sage?