Playground

This is the five octahedra and the corresponding five 90-90-90 triangles of the pentagramma mirificum, with just one octahedron emphasized.            

Here are two animations of the five octahedra and the 90-90-90 triangles, where just two octahedra are emphasized, but two which interact differently as the pentagramma changes.

Here is the pentagramma mirificum projected onto a plane; the first two sliders change the pentagramma, and the other two sliders change the location of the tanglent plane the pentagramma is projected onto.