  A novel understanding of scattering amplitudes in terms of on-shell diagrams
and positive Grassmannian has been recently established for four dimensional
Yang-Mills theories and three dimensional Chern-Simons theories of ABJM type.
We give a detailed construction of the positroid stratification of orthogonal
Grassmannian relevant for ABJM amplitudes. On-shell diagrams are classified by
pairing of external particles. We introduce a combinatorial aid called `OG
tableaux' and map each equivalence class of on-shell diagrams to a unique
tableau. The on-shell diagrams related to each other through BCFW bridging are
naturally grouped by the OG tableaux. Introducing suitably ordered BCFW bridges
and positive coordinates, we construct the complete coordinate charts to cover
the entire positive orthogonal Grassmannian for arbitrary number of external
particles. The graded counting of OG tableaux suggests that the positive
orthogonal Grassmannian constitutes a combinatorial polytope.
