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Help with MW63
Posted: Sun Mar 10, 2013 1:45 pm
I’m looking for some help with the 16th stellation of the icosidodecahedron (MW 63). This is a vertex-connected polyhedra. I’ve chosen special colour arrangement 2 (dodecahedral) so that the pentagonal faces are all the same colour, but stuck on what to do about the backs of the cells. The easy option would be to colour these all the same – black or white, say, but I wonder if there is a better (more aesthetically pleasing) option that uses the same colour scheme as the front faces ? I’m having a bit of trouble visualising this, so I’d appreciate any suggestions you might have.
These vertex-connected models are a bit awkward to build and take a lot of time, otherwise I’d consider building a partial prototype.
Posted: Sun Mar 10, 2013 2:06 pm
I think I've worked it out: the back face of each side of a star arm should be the same colour as its front face.
Posted: Mon Mar 18, 2013 8:33 pm
The backs lie in the 20 face planes of the icosahedron. These correspond to the 20 vertices of the dodecahedron, so matching them with the 12 pentagonal faces doesn't work.
You could match the corners of each triangle to the 12 faces, which is of course the "same back and front" solution you found.
Unless of course you have (12 + 20) / 2 = 16 colours of card....
Posted: Thu Mar 21, 2013 7:19 pm
Thanks Guy. I still can't visualise it, but I think you are right. I coloured one of the back faces with Stella and five others were coloured the same. As there are 120 of these pieces, that suggest 120/6 = 20 planes. I think I'll set them all to white.
Posted: Fri Mar 22, 2013 12:58 pm
Yeah, being a stellation of the icosidodecahedron, some parts lie in the pentagonal face planes (the planes of a dodecahedron) and some in the triangular face planes (the planes of an icosahedron). In this case the outer faces lie in the dodecahedral planes and the inner faces lie in the icosahedral planes.
As to colouring, yeah you could just use the same colour on the outside face as the inner face that shares an edge with it. You could also use Stella's icosahedral colour arrangement 1 if you want lots of colours altogether. Personally I prefer the geometry and symmetry to speak for itself and go for fewer rather than more colours, so I'd do it in just two colours I think!
By the way, do people know that you can easily load any of Wenninger's stellations in Stella? They don't appear in the list, but you can still use "File->Polyhedron List" and type "W63" to access this model. If you don't already have a stellation view open it will ask you if you want one.
You've got me interested in attempting a model of this myself now. I've yet to make a vertex-connected model. What method do you use to keep it together? It occurs to me that putting fishing line through the vertices could at least hold the points together, though not necessarily in the right orientation on its own. With this model however, I think just the fishing line would be enough, at least in theory if not in practice, to hold everything in place.
PS. Here's a picture for anyone who doesn't know what we're talking about.
Posted: Fri Mar 22, 2013 2:03 pm
Thanks for your comments. I'm not sure if this will work, but we discussed options for building vertex-connected polys here:
http://www.software3d.com/Forums/viewto ... highlight=
If that doesn't work, look for my post "Delicate Flower or Triffid ?". After that, I stayed well clear of this type of model, and having read it again I'm beginning to wonder if I should try persevere with this one.
At the moment, the project is dormant (I had a batch of fancy card that I wanted to try out, but it wasn't suitable for this model, so I started work on the Great Icosahedron last week), but I expect to return to it soon.
I remembered your suggestion about fishing line and I intend to try that out along with some similar options. For this particular model, I could probably get away with just reinforcing a subset of the cells - just enough to add a bit of strength. Also, with the icosahedron stellation, I had the cells joined in threes, so it was more difficult to thread them together. And the cat kep eying up the thread!
Posted: Fri Mar 22, 2013 2:48 pm
Oh yeah, well making a vertex-connected model has been in the back of my mind for a long time. I'll do it sooner or later. Your previous model would indeed be trickier I believe, and the thread would not be enough to hold it in place. With W63, thread should be enough, in theory. Maybe glue at each point can be added as an afterthought if necessary.
I know what you mean about the thread pulling away from the point. I imagine it gradually ripping through the paper! And I agree that some other sort of thread would absorb glue better than fishing line, but at least fishing line will never break. Maybe it could be threaded around and knotted inside.
With W63 maybe some sort of solid wire could be used, since edges align across the points. There's probably a very thin but strong wire available. Still have to attach it robustly to the paper along the inside edge somehow.
Posted: Mon Mar 25, 2013 7:53 am
I made a similar model where the top vertices of the pentagrammic pyramids are pointing towards the center:
I glued the model with UHU hart, no threads were needed.
Posted: Tue Apr 09, 2013 6:35 pm
That's a great model, Ulrich - made with such precision. I never considered using balsa cement, but this is the second time I've seen it recommended recently, so I'll get some UHU Hart and give it a try.
Posted: Fri Jan 31, 2014 9:53 am
It is 10 months since I first opened this topic, and after a couple of false starts and long periods "in the wilderness", I finally have something to show:
<a href="http://s1135.photobucket.com/user/polyp ... 9.jpg.html
" target="_blank"><img src="http://i1135.photobucket.com/albums/m62 ... 29f1f9.jpg
" border="0" alt=" photo MW63small_zps2729f1f9.jpg"/></a>
Unfortunately, I forgot to remove the little post-it labels that help me keep track of the different sections. The cat wouldn't budge. The vertex joints are reinforced with steel pins, so the model is quite robust (held in place with UHU Hart balsa cement, which is great). Thanks for the suggestions.
Posted: Fri Jan 31, 2014 9:57 am
Looks like I messed up there. Lets try again:
Posted: Fri Jan 31, 2014 11:27 am
Looks great, especially with the colouring of the pentagons.
PS: I wouldn' trust the cat!
Posted: Fri Jan 31, 2014 12:06 pm
Thanks, Ulrich - and you were right about the cat!
Posted: Sat Feb 01, 2014 5:08 am
Looks great! How are the pins held in place? They'd need to sit under a fold/join in the paper, but what keeps them in that fold? I wouldn't have thought paper/wood glue would do a great job.
Posted: Sat Feb 01, 2014 10:42 am
In this model, we are lucky, because the pins just join TWO sections, not more. Of course, they sit along the fold between each pair of triangles that constitute a star arm (the pairs of triangles that are on the outside). So the pins join two parts of the large pentagonal faces.
UHU hart balsa cement is fine stuff. It would probably do the job on its own, but I also added a tiny triangular piece of card which was folded in two. I placed this well into the vertex, just on top of the pin. For early sections, I also did the same on the joining vertex, but as the model progressed I found that my approach did not give the best (neatest) results. I still used the technique for the first pin, and also the second when I could access it easily, but sometimes I relied just on a blob of glue in the second section and sometimes I screwed up a tiny wodge of kitchen paper and pushed this into the vertex on top of the pin.
Originally, I did the obvious: I constructed the outer (coloured) section of each star first and then stuck on the (less visible) back pieces, but I found it almost impossible to align the inside pieces accurately. So I reversed my approach and built the inside star first. I was a bit surprised, but this gave much better results. As the model was built up, the pieces that had been assembled all had projecting pins, waiting for their partners.
Should have taken some snaps, but couldn't wait to finish it !