Shelling order of a simplicial polytope

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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]