Hello!
I love making large convex paper polyhedra models. So far i made the Archimedian and Catalan solids and also models for stI, gtI, ttI, etI, kdtI (some Conway Operations on the truncated icosahedron). I would like to make a model for the remaining btI=trtI and its dual, furthermore for the zonohedrified truncated icosahedron and a (5,3) Goldberg polyhedron. These polyhedra are very big (the Zonohedron has 870 rhombic faces) and I couldn't find their nets anywhere. Therefore I consider to buy Stella3D.
My question is: Is Stella3D capable of generating nets of the polyhedra I mentioned? Is there any limit how big the net can get (I mean the complete, connected net, not just a list of all the disjoint faces)? If I adjust the size to be 1cm or 0.7cm per edge - the complete net certainly doesn't fit on a DINA4 Paper - will the program be capable of deviding the net in a smart way, lets say on 2,3,4 sheets of paper?
Thank you very much in advance!
Kind regards, Gokusa22
Nets of large polyhedra
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robertw
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Re: Nets of large polyhedra
Hi, first you're probably after Great Stella or Stella4D. There isn't one called Stella3D.
Great Stella has various ways to create zonohedra, so yes you can create that one with 870 faces.
Goldberg polyhedra are duals of geodesic spheres. Stella can create duals, but it can only directly create class 1 geodesics, whereas the 5,3 you asked for is a class 3, so you'd probably have to find a version of that to import.
Stella also doesn't support Conway notation yet, though I'd like to add it someday. But you could generally make them with a combination of subdividing faces followed by faceting, or other ways, but it's not always obvious. For btI though, Stella already has the following model in its "Near Miss" section:
and you can use the "Morph Duals by Truncation" view to truncate it at some point, like this:
Hmm, result is a bit out of shape though. I tried to make the faces more regular but didn't get it to work very well.
In summary, aside from the zonohedron you're asking for some tricky ones which may need to be imported.
Onto nets... Stella doesn't technically have a limit on how many faces it can connect together into nets, but in practice it may fail to add all the faces, and put some in separate nets. To be honest, construction is easier with multiple nets for large models. Otherwise you get very small angles for nets between some faces, and having the whole net hanging off while gluing the initial faces together makes it difficult.
Stella has a menu item "Nets->Maximum Faces per Net" where you can set a maximum. If it tells you the nets are too big when printing, you can try setting that to limit the number until the smaller nets fit. It can automatically shrink nets to fit, but not automatically split them, as you get the nets you see on-screen before printing, but setting the maximum faces is the easiest blunt instrument for the job (you can also control exactly which edges connect at a finer level if you need to).
If these are paper models you may want to consider adding struts inside too to give the model strength. Large convex models tend to dent easily. Stella can hel pwith that too.
Great Stella has various ways to create zonohedra, so yes you can create that one with 870 faces.
Goldberg polyhedra are duals of geodesic spheres. Stella can create duals, but it can only directly create class 1 geodesics, whereas the 5,3 you asked for is a class 3, so you'd probably have to find a version of that to import.
Stella also doesn't support Conway notation yet, though I'd like to add it someday. But you could generally make them with a combination of subdividing faces followed by faceting, or other ways, but it's not always obvious. For btI though, Stella already has the following model in its "Near Miss" section:
and you can use the "Morph Duals by Truncation" view to truncate it at some point, like this:
Hmm, result is a bit out of shape though. I tried to make the faces more regular but didn't get it to work very well.
In summary, aside from the zonohedron you're asking for some tricky ones which may need to be imported.
Onto nets... Stella doesn't technically have a limit on how many faces it can connect together into nets, but in practice it may fail to add all the faces, and put some in separate nets. To be honest, construction is easier with multiple nets for large models. Otherwise you get very small angles for nets between some faces, and having the whole net hanging off while gluing the initial faces together makes it difficult.
Stella has a menu item "Nets->Maximum Faces per Net" where you can set a maximum. If it tells you the nets are too big when printing, you can try setting that to limit the number until the smaller nets fit. It can automatically shrink nets to fit, but not automatically split them, as you get the nets you see on-screen before printing, but setting the maximum faces is the easiest blunt instrument for the job (you can also control exactly which edges connect at a finer level if you need to).
If these are paper models you may want to consider adding struts inside too to give the model strength. Large convex models tend to dent easily. Stella can hel pwith that too.