Those billboards are an alternative (the more traditional) impostor type. The octahedral impostors replace these billboards with a geodesic polyhedron of octahedral symmetry. Basically it subdivides the sides of an octahedron to approximate a sphere.

Not really. The octahedron defines the positions you pre-render the impostors from. The actual rendering uses a flat plane (like a regular billboard) but with a parallax shader and depth offset to make it look bent.