### Connecting Things, Page 1: Five Octahedra

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:

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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:

The same without a sphere:

With the pentagramma mirificum:

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