From the standpoint of what has been seen so far, let us return to a previously stated characteristic of the pentagramma. It was seen that every pentagramma mirificum, not just the regular, will define five triangles whose sides and angles are all 90 degrees:

(*Note: You may need to move one of the sliders to get the triangles to appear)

Recall from the investigation above, triangles made of three 90 degree sides will result from the division of the sphere that generates the octahedron:

It is then true that any pentagramma mirificum will define five different octahedra (one from each of the five different 90-90-90 triangles), whose orientation with one another depends on the irregularity, or regularity, of the pentagramma mirificum defining them.

The five 90-90-90 triangles, and the five octahedra: