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Topological Great Dodecahedron

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This is a stylized version of the great dodecahedron. The idea is that only true edges of the polyhedron should connect. The false edges that normally appear in a model where faces intersect but don't share an edge have been removed by hiding parts of each face, allowing the faces to pass through each other without collision. I call this a topological model, as it highlights the true topology of the polyhedron. This lets you better see the internal structure of the polyhedron.

Here's a great dodecahedron in Great Stella, showing in colour the parts that will remain of each face. The grey areas have been cut away. In the final model, it's quite hard to see the original great dodecahedron!
The finished model in Great Stella. Here we have a solid model, unlike my paper model whose sides don't have any thickness to them. The parts I used are coloured, while the other faces are black. In fact you can print the nets without even making a solid model like this. Instead, just use Faceting mode to design the faces. Facets appear in the nets straight away, without having to complete the model. These faces were created by loading a great dodecahedron, then using "Poly→Subdivide Faces" with 16 subdivisions, and finally using the additional vertices in Faceting mode to design the final faces.
Here's one part. You'll need 12 of these.
They attach only at the small outer edges. Use small tabs so as to be unobtrusive, since they will be visible in the final model.
Half the parts in-place. Notice that the pink part is not actually attached to anything yet. Be sure not to glue anything together till you're sure it won't prevent you putting subsequent pieces in place!
All the parts are in place here, though a bunch of gluing remains.
The finished model from another angle.
A close-up of the finished model.

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