This is about transformation of tetrahedra. Edges are rotated about a line between their midpoints and the origin. This is represented in the video animation linked below as in the form of Tensegrity. Compression elements are shown in color, while tension elements are shown in light grey, representing strings or wires. Edges are shown rotated through a sequence of skew positions, to a configuration of 3 pairs of parallels orthogonal to each other. Scenes shows some illustrations of how the sequence is derived, and views of the full sequence. Some of the directions that appear as white in these illustrations have been colored for clarity in the video. Struts that begin as edges of a Tetrahedron are shown rotating through this parallel orientation to arrive at the other orientation of Tetrahedron. This much of the transformation is labelled the “A set.” Continuing the rotation, the strut passes through the “B set,” which includes an alternate orientation of the 3 pairs of parallels configuration, and ends at the starting place.
Related transformations can be seen Here and Here
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While the models and animation above accurately represent the metrics of the tensegrities, the model below more accurately shows how such models are constructed physically. Pointed sticks with correct proportions of compression element to tension element are compared in Scenes with square ended sticks, which must be longer by the thickness of the sticks to maintain correct proportions.
