# How to obtain the vertices of the faces of a polyhedron in the cycling order ?

I wanted to transfer informations from sagemath to Asymptote and draw the faces of a dodecahedron. So according to the documentation I code

```
Dodec=polytopes.dodecahedron()
F1 = Dodec.faces(2)
fa=[f.ambient_V_indices() for f in F1]
fa
Vdodec=Dodec.Vrepresentation()
Sdodec=[(round(Vdodec[i][0],2),round(Vdodec[i][1],2),round(Vdodec[i][2],2)) for i in range(len(Vdodec))]
show("fa= ",fa)
show("points = ",Sdodec)
```

If I have understood the documentation `fa`

gives the vertices implied in a face. Those vertices are numbered according to the order of the `Vrepresentation()`

of `Dodec`

as written in the doc :

`"The faces are printed in shorthand notation where each integer is the index of a vertex/ray/line in the same order as the containing Polyhedron’s Vrepresentation()"`

. So (15,16,17,18,19) is a face composed of the points :

```
p15=(-0.76, 0.76, -0.76),
p16=(-0.76, -0.76, -0.76),
p17=(-1.24, 0.47, 0.0),
p18=(-1.24, -0.47, 0.0),
p19=(-0.47, 0.0, -1.24),
```

And this is true. But here comes the problem : as I understand it, the face should be the closed cycle `p15--p16--p17--p18--p19`

. But transfered in Asymptote, I discovered that the true order should be
`p15--p19--p16--p18--p17`

. The same type of error seems to be the case for each face (good composition but bad order).

So here is my question : is there a command which gives the good order of the vertices which define a face or is it an error because the vertices should be given in the good order ?

(Hope that this time there is no element missing in the code)