topological

[michaelhislop]

Hi fellow STELLA users.

I have spent many Hrs trying to make some progress in understanding TOPOLOGICAL models. I have read all I can find on the web and locked up my computer on numerous occasions.
I have worked with Great Dodecahedron and Topological Great Dodecahedron trying to make sense of the following.
” 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.”
Is there some further information I have not yet come across?
Can some kind person give some further advice?
Thanks Mike Hislop
[/list]

[robertw]

For reference, here's the model you're talking about: http://www.software3d.com/TopoGD.php

Can you be more specific about what you don't understand?

I came up with the term "topological model" myself, so you may not find many other references to it, but I didn't invent the idea. George Hart for example has 3D-printed a number of sculptures based on this idea. I'm not sure what he calls it. I originally just called them hollow models.

First one needs to understand that the great dodecahedron consists not of the apparent external triangular faces, but rather 12 intersecting regular pentagons. A topological model cuts away parts of faces so that the "fake" edges are avoided, ie the concave edges apparent when looking at the model, which are not true edges of the polyhedron, rather just intersections as faces pass through each other. In the topological model, faces are only attached at their true edges.

The two images you refer to, and the main image, are aligned and coloured the same way. Hopefully you can see where the model emerges from once the grey parts are cut away.

[michaelhislop]

Hi Richard, thanks for your prompt reply.
George Hart appears to refer to these models as Abstract. It was finding his models that prompted me to find out how to design such models which led to Stella.

I assume your Topo models are only the tip of the iceberg.

I understand and have identified the polygons you refer to but can not understand the polygons are divided so as to change the colours.
I understand hiding the remaining sections of the model. I have tried Poly Subdivide Face, assuming this is the process required.
If the subdivision is higher than say 8 my computer locks up. In other models the Show Stellations Vertices appear but not in the Great Dodecahedron or its Unfolded Net.
Is this process worthy of a tutorial as it appears other users have not ventured down this path?
It is my intention to develop these models into Kinetic Motion Art Works.
Another question: Is it likely the nets can be exported as a vector file for CNC laser?
I cut my Kinetic models in my laser produce miniature kitsets model railway dolls houses etc.

Thanks Mike

[michaelhislop]

Hi Richard

I have success in replicating The Topological Great Dodecahedron with some minor variations.

Now on to more complex shapes I hope.

regards Mike

[robertw]

Step 2 of the Hollow Sphere Tutorial has some steps that are relevant here: http://www.software3d.com/TuteSpherical.php.

But also, you can just print the new parts directly from the faceting view, without having to build a finished model requiring a thickness for the parts.

Yes I use subdivide faces, and then Faceting mode and Faceting view to create the cut-away faces I want. I try to use the least level of subdivision that works. Higher levels give you more vertices to play with, but make it harder to figure out which vertex is which.

I would hide any net and stellation views during construction, and show vertices rather than stellation vertices. Computing nets might be what locks up for you at higher subdivisions, but you don't need nets at that stage.

[michaelhislop]

Thanks for your help Richard

[robertw]

Thanks for your help Richard

That's Robert, by the way