At first I wanted to scale the “Octahedron Expanding Into Cuboctahedron”, but I didn’t like the result, so I decided to recreate it in FreeCAD instead, and I loved how it turned out. After that I searched for other possible geometric shapes, and the closest ones I found without over-complicating the geometry were the Icosidodecahedron and the Rhombicosidodecahedron, so I decided to add a pentagon face, and here we are. I'm satisfied with both models.
I’ve used varsets to design all the bodies so I can change the sizes later on, and I also made “supported” versions. I'm not a real or pro designer, so please don’t judge that part too harshly.
For “Octahedron Expanding Into Cuboctahedron”:
8 × frame_v2
12 × joint_v2
For “Icosidodecahedron Expanding Into Rhombicosidodecahedron”:
20 × frame_v2
12 × frame_v3
60 × joint_v3
The author remixed this model.
I recreated it in FreeCAD using parametric varset setups. This version is fully rebuilt and also includes a new shape: an Icosidodecahedron expanding into a Rhombicosidodecahedron. The frames and joints are redesigned to extend the concept.