  Let $\cal P$ be a non-degenerate polar space. In [I. Cardinali, L. Giuzzi, A.
Pasini, "The generating rank of a polar grassmannian", Adv. Geom. 21:4 (2021),
515-539 doi:10.1515/advgeom-2021-0022 (arXiv:1906.10560)] we introduced an
intrinsic parameter of $\cal P$, called the anisotropic gap, defined as the
least upper bound of the lengths of the well-ordered chains of subspaces of
$\cal P$ containing a frame; when $\cal P$ is orthogonal, we also defined two
other parameters of $\cal P$, called the elliptic and parabolic gap, related to
the universal embedding of $\cal P$.
  In this paper, assuming $\cal P$ is an orthogonal polar space, we prove that
the elliptic and parabolic gaps can be described as intrinsic invariants of
$\cal P$ without making recourse to the embedding.
