How to create a solid icosidodecahedron

[incognito]

I am pretty new to Pro/E. I am trying to create a solid icosidodecahedron (an Archimedean solid), and so would appreciate any help you can give me as to how I can do that. Thank you very much.

 

[vlad1979]

This is a good question.


This would be a nice little thing todo for that competition that Zaki (I think) mentioned in a previous thread.

 

[incognito]

Vlad, competition is good, but I am just looking for a solution. If you know one, could you please send me a PM so that you would not tip the competitors? Thank you.

Edited by: incognito

 

[prohammy]

Vlad,


Another option (maybe) for a competition, rather than just an icosidodecahedron, how about a family of Archimedean solids....


Just a thought

 

[prohammy]

Vlad,


Meant to include this link


http://mathworld.wolfram.com/ArchimedeanSolid.html


Kev

 

[Israr]

Just to comment; an acceptable solution would be one which can be developed in sheetmetal. I mean cuttinga sphere by trial and error will be no solution.


Israr

 

[vlad1979]

it was just a thought about that competition Zaki suggested. This is a long word, should be used in spelling competitions

1. Israr is right if you need to manufacture this then you will most definitely need to do this in sheetmetal.
This is how it should look in flat form:
[url]http://en.wikipedia.org/wiki/Image:Icosidodecahedron_flat.pn g[/url]
You could make that in sheetmetal then bend back the faces. !?!



2. for sheetmetal you can go with a different approach. You could try to makeit like this:
[url]http://en.wikipedia.org/wiki/Image:Icosidodecahedron_vertfig .png[/url]



3. But if you need only a dummy solid, you could try also to make the point on corners then make surfaces between them, solidify, I guess.
I think this points are giving you the corners (not sure what they are for?):
[url]http://www.scienceu.com/geometry/facts/solids/coords/icosido deca.html[/url]



4. There is a generating triangle that gives you the geometry, if you can duplicate that somehow, you could end up withthe anicosidodecahedron.
[url]http://www.scienceu.com/geometry/facts/solids/L-icosidodeca. html[/url]


These are all just thoughts, right now I have no idea how to do it, never done this. I would try to model it but these days I'm pretty busy. But give it a try see if something comes out.

maybe will look like an icosidodecahedron.

 

[SRINIVASANIYER1]

VLAD,


Thank you very much for the links. Quite informative. I have been away from mathematics for a long time now. World has really changed with the internet.

 

[mcgowanp]

Ingonito, curse you for asking this question. I had a long night last night, I even made a hand model of it!!! I'm gonna need serious mental adjustments after this one. anyway heres my attemp at it.


2007-02-22_070858_icosidodecahedron.prt.rar


There's some nice effects to be had with shelling this component and adding some simple rads!!


View attachment 3190

 

[vlad1979]

nice.


must have been a very long night.

 

[incognito]

mcgowan, I am unable to see the part. When I open it my Pro/E 3.0 gives an error about an invalid format. Help says this is about non-binary transfer of data between Unix and Windows. It offers to correct it which I do. Then I only see the part name with no features. Pro/E says:
<div style="margin-left: 40px;">Regeneration completed with 60 suppressed feature(s) or component(s).
</div>If I try to regenerate again, then I get:
<div style="margin-left: 40px;">Line 19 part ICOSOHEDRON-DIE: Invalid left side of assignment
</div><div style="margin-left: 40px;">Part 'ICOSOHEDRON-DIE' not changed since last regen.
</div><div style="margin-left: 40px;">WARNING: Some constraint relations are no longer satisfied in ICOSOHEDRON-DIE.
</div>

 

[mcgowanp]

if you go to your settings for you model tree and check the little box to show suppressed features then the surpressed item will come up. If the features are suppressed then you will have truouble with the realtions.


I am using WF2 so not sure if there will be any issues with some of the features that I used.

 

[incognito]

mcgovanp, I got it! Started fresh and opened it without a glitch. Sorry for initial confusion!

I will take time off now to study what you have done. Thank you very much. It looks beautiful, doesn't it?

 

[puppet]

incognito

Nicely done!

Can i ask where you got the values for angle1 and angle2?

 

[incognito]

I am studying the design, and I've got the same question, actually: how did you come up with the values for angle1 and angle2? I have a feeling that with the angles like that there can be a gap somewhere that is usually very hard to spot.

Another question is this: If I need to make icosidodecahedrons routinely, what do I do? Will I have to make them with this lengthy procedure? Or....

There comes the third question: Can we do the same programmatically? Define programmatically all corners and edges, constraints and relations, and connect them in the right way? Could someone give me an example for icosidodecahedron?

Thank you all very much for your ideas and help.

 

[magneplanar]

In the mathworld link they have patterns for the unfolded shapes. could this then be made using sheetmetal? IE: cut out the pattern and then make the necessary bends?
not exactly a slow process to be sure hahah.

 

[mcgowanp]

There is a formula for getting the angles, I'll see if I can find my scriiblings on this. attached is updated one with a parameter for length. to get different size you want then change the pentangle_length parameter to the required length.


There arent any gaps in it, because it was made from flat fills if there were any gaps between these surfaces then it would not merge or solidify. However one of the requisites for being a archimedian solid is that every length should be exactly the same, I seem to have a variance of +.00002 -.000001.


Heres the updated file.


2007-02-23_061044_icosidodecahedron.prt.rar

 

[vlad1979]

Searching the net for informations about icosidode...bla..bla (long word, I can't even spell it

), found that at the origin it's a icosahedron that has the corners sliced.


http://polyhedra.mathmos.net/entry/icosidodecahedron.html


Now, how do you make a icosahedron?

It turns out you can make it pretty easily if you "know" it has to do with the "golden_ratio". Look where it says cartesian coordinates:


http://en.wikipedia.org/wiki/Icosahedron


Now, what's a golden ratio. Turns out it's everywhere:


http://en.wikipedia.org/wiki/Golden_ratio


So I made a icosahedron and then I sliced it's corners at the middle of the edges. And I got a icosidode..........


There is a parameter "length" that gives the egde length, modify that:


2007-02-24_070954_icosidodecahedron.prt.rar


I never done surfacing, this is my first attempt so maybe itcan be done with fewer features.

 

[mcgowanp]

Well done Vlad, a much more informed approach than mine!!! Thats a real nice technique, nice and simple.

 

[vlad1979]

And a sheetmetal version:


2007-02-26_002739_icosidodecahedron_sheetmetal.prt.rar


I'm not very happy of the way it turned out. Until the last bend it looked OK. I have the same angle between faces as Mcgowanp, but when I did the last bend the 2 halfs are intersecting too much. I don't want to "invest" too much time to see what's wrong. But it can be done in sheetmetal.


incognito: in a previous post I added on this thread I think there is a link to a formula of some sorttoobtain the corners. So maybe you can use that into a relation:


http://en.wikipedia.org/wiki/Icosidodecahedron


Or you can figure out the formula usingthis link. These are the corners coordinates. Add these to a point table file. ( I did and it looks like it may be a icosido...)


[url]http://www.scienceu.com/geometry/facts/solids/coords/icosido deca.html[/url]