Edges of an Octahedron transforming to edges of a Cube. In this series of models edges are shown rotating about radial lines from the origin to their midpoints. The first model shows a template as a “fan” of colored struts that are the directions of rotated edges, in relation to Octahedron and Cube. These models are all chiral, there could be another set of directions that mirror these. This series depicts the transformation in Tensegrity mode, with the rotated edges representing compression elements, or sticks.
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This shows an Octahedron and a Cube that share midpoints of their edges, as frame of reference.
The first stage in the transformation, showing olive colored struts rotated from edge positions. Octahedron is included as reference frame.
Second stage, turquoise struts.
Third stage, white struts.
In this model, the rotated edges have become oriented into four parallel sets of three, aligned with 4 axes of symmetry. As parallel groups, these struts can be extended as beams. In this form, the tension network is aligned with edges of a Truncated Octahedron.
An animation of this transformation can be seen in this Video
A continuation of this series can be seen at Twelve Edge Transformation Part 2
A precursor of this series can be seen Here