How to create a solid icosidodecahedron

[Zaki]

Hey


I think I had posted a competetion months ago, u can search it by the name of lota competetion. I will try to post the part tommorow.

 

[Zaki]

here is the address guys


[url]http://www.mcadcentral.com/proe/forum/forum_posts.asp?TID=30 206&KW=lota[/url]

 

[ossito16]

Hi all,


I was thinking about taking that image of the iso in a flat state. [url]http://en.wikipedia.org/wiki/Image:Icosidodecahedron_flat.pn g[/url]


Then converting it to a dxf or some format I can import into sheetmetal as a sketch. Then figure out the angles needed and use bend features in sheetmetal.

 

[mjcole_ptc]

Googled it like everyone else. and it's a cool geometric object.

You could model a regular dodecahedron and and then make a small V shaped cut sketched on a plane bisecting adjacent pentagonal sides and the pattern it. In fact I've done many hedra to test out different CAD systems capabilities and I think I''ll add the model to my challenge list.

 

[wcwyder]

I know you Pro/E users don't want to hears this, but I created an
Icosidodcahedron using a Student Edition of SolidWorks in about 30
minutes. I used a single pentagon and a single triangle, both
with beveled edges, using circular patterns and duplication
in assenbly mode.

 

[mjcole_ptc]

The way to get the equations for the angles between the faces by equation is involved but quite simple in principle using triangles. For a Pentagon you can divide it in two 5 isosoles triangles with an angle of 72 degrees in the center and (180-72)/2 = 54 degrees in the two other corners you also know that the triangular faces are equilateral with equal length sides and 3 equal angle of 60 degrees each. If you want to use Excel to develop the solution remember the 180deg = pi*r conversion or you can use a scientific calculator or even your base sketch to develop your equations to make things easy make all of the side lengths equal to 1 unit using geometry and trigonometry you can get the length from side to vertex of the equilateral as C = A * sin (60) where A is the side length and equals 1. Then you need to take the difference between the distance from the top pentagon's side edge to the center and the distance D from the vertex of a second pentagon whose sides are drawn between the outer vertices of the first set of 5 triangles that are rotated off the initial pentagonal face lets call this C and take the arc or inv cosine of D/C to get your angle.

The angle will be 37.377----- depending on how exact you want to be.

To create the model you can create a bunch of fill surfaces creating triangles with a datum angled at the calculated angle and using the use edge and equal length options and patterns of 5 features at an angle of 72 degrees. You only need to create half the faces then do a transformation with two angulardirections. one of 180 degrees to mirror the object about the center plane and then to rotate it by 36 degrees so the triangular face meet up with the pentagon faces on the other half.

On each side you'll get 6 pentagons and 10 triangles to make up a total of 32 faces.

I'll probably post my model to this site tommorow.
Here's a picture describing the math used to calculate angles.

[url]http://www.imagestation.com/picture/sraid225/p5ae6bc51d7a6cc 2f25f261947d682858/ea4ec842.jpg [/url]

[url]http://www.imagestation.com/picture/sraid225/p7a3c9bd4f4eb0a 193f5831dc17a87fd6/ea4eb9c8.jpg [/url]

Michael




Edited by: mjcole_ptc

 

[mjcole_ptc]

Here's a link for all you Geometry Lovers or (GeoGeeks)

They are easy to use and I plan to make an Assembly with the pieces I have made on Pro/E. Most of us have approached building these shapes as part models which makes sense for creating Solid Dice. I'll post a pic when I finish my icosohedron assembly first then I'll use an inheritance feature to turn my 3 sided part into a 5 sided one.
<a href="http://www.geoaustralia.com/english/geoshapes/Index.htm" target="_blank">
http://www.geoaustralia.com/english/geoshapes/Index.htm</a>

Michael


Edited by: mjcole_ptc