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Using the appropriate packing pieces, each of Plato’s solids can be fitted into the same 3D hull.
The colouring of the 3D hull is the same for each model and on loading all the models are aligned in the same way and at the same scale.
There are multiple ways that the Cube, Octahedra, Icosahedra and Tetrahedra solids can be aligned within the 3D hull.
Only one example of each solid has been selected to keep these representations as simple as possible. The alternatives could be found in the physical model by rotating the “packing pieces” within the trackball hull.
The physical Tetrahedron model requires 4 “packing pieces” to fit it into the 3D hull. (The other models can be built/disassembled using only two packing pieces.)
With many thanks to Scott Vorthmann, John Kostick and David Hall.