Edges of an Icosahedron transforming to edges of a Dodecahedron. 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 Icosahedron and Dodecahedron. 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.

A 3D design created in vZome. Use your mouse or touch to interact.

In the first stage of this transformation, edges of Icosahedron are rotated to maroon colored orientation. Icosahedron is shown as reference frame.

Second stage is sulfur colored orientation.

Next stage, further askew from Icosahedron, is olive colored.

Purple orientation. If extended, these directions can intersect as interlinking equilateral triangles.

At this stage, the struts are rotated into alignment as 6 sets of parallel groups, 5 in each. These groups, or beams, are oriented around 6 axes of icosahedral symmetry.

An animation of this transformation can be viewed Here

A continuation of this series can be seen at Thirty Edge Transform Part 2

A precursor of this series can be seen Here