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Topological Dodecadodecahedron

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This is a stylized version of the dodecadodecahedron. 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 a true edge have been removed by hiding parts of each face, allowing the faces to weave past each other without collision. I call this a topological model, as it highlights the true topology of the polyhedron. This gives you a better understanding of the internal structure of the polyhedron.

Here's a dodecadodecahedron in Great Stella, showing in colour the parts that will remain of each face. The dark grey areas will be cut away. In the final model, it's quite hard to see the original dodecadodecahedron!
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. I kept the coloured parts from this image, leaving out the black faces. 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 dodecadodecahedron, then using "Poly→Subdivide Faces" with a high level of subdivisions, and then using the additional vertices in Faceting mode to design the final parts.
Here's all 24 the parts ready to go.
There are two different types of part required, as seen here. 12 copies are required of each.
Each pair of connected parts attach at two locations. These are at the start and end of the original dodecadodecahedron edge.
It's not too hard to make sure the parts weave past each other correctly, but do take some care. I started with one of the smaller pieces and attached 5 larger parts around it. Put a sixth large piece in place below the original small part (nothing to glue to yet). Then you can glue in 5 more of the smaller part.
Here's what it looks like from inside at this stage.
Continue gluing large parts into the second half of the model. The final large part can be sat near the top (the model now sitting on the small part we started with) and twisted down into place between the other larger parts. Take care that everything weaves past each other correctly. Then glue the final small parts into place.

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