1 | initial version |

Dear Guillermo,

The answer to your question is yes. Here is an illustration with the octahedron:

```
sage: P = polytopes.octahedron()
sage: Facets = {f.ambient_V_indices():f for f in P.faces(P.dimension() - 1)} # Create the vertices-indices-to-facets dictionary
sage: P.is_simplicial() # Check that P is simplicial, so we can get the boundary complex
True
sage: C = P.boundary_complex() # Create the boundary complex
sage: Order = C.is_shellable(True); Order # Get a shelling order
((0, 1, 2),
(1, 2, 5),
(1, 3, 5),
(0, 2, 4),
(0, 1, 3),
(0, 3, 4),
(2, 4, 5),
(3, 4, 5))
```

Finally, we can get the actual sequence of facet using our dictionary.

```
sage: Facet_shelling = [Facets[indices.tuple()] for indices in Order]; Facet_shelling
[A 2-dimensional face of a Polyhedron in ZZ^3 defined as the convex hull of 3 vertices,
A 2-dimensional face of a Polyhedron in ZZ^3 defined as the convex hull of 3 vertices,
A 2-dimensional face of a Polyhedron in ZZ^3 defined as the convex hull of 3 vertices,
A 2-dimensional face of a Polyhedron in ZZ^3 defined as the convex hull of 3 vertices,
A 2-dimensional face of a Polyhedron in ZZ^3 defined as the convex hull of 3 vertices,
A 2-dimensional face of a Polyhedron in ZZ^3 defined as the convex hull of 3 vertices,
A 2-dimensional face of a Polyhedron in ZZ^3 defined as the convex hull of 3 vertices,
A 2-dimensional face of a Polyhedron in ZZ^3 defined as the convex hull of 3 vertices]
```

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.