A simple dodecahedron

Replies to This Discussion

Permalink Reply by nikos tzar on April 2, 2015 at 10:19am

Hello Judson,

If your student doesn't want to use a plugin (weaverbird, lunchbox,...) then I understand that she wants to study the geometric rules behind this solid. So, in my opinion, this is the part that you should do with her and then ask for help with the GH definition. Having someone do this study and create the definition for her will not provide much more knowledge than using a plugin component. 

As you can see in this chalenge that was posted in the coffe & GH group, there are many ways to draw a platonic solid. If you figure your approach you will definitely get help setting up the GH definition.

cheers, nikos

Permalink Reply by Judson Swets on April 3, 2015 at 12:09am

Excellent advice.  I will start with the challenge you posted.  Studying the solutions to the icosahedron challenge will help me better understand the components I'll need for the dodecahedron and others.  I will point my student the same way.  She's the kind of person that wants to do it herself and understand every step.  

Thank you, Nikos.   I likely wouldn't have found these files without your help.  

Judson

Permalink Reply by nikos tzar on April 3, 2015 at 5:40am

What I was trying to suggest is to not think about GH components just yet, but rather define the problem in geometrical terms as a first step.

For example: 

1st approach: Start from a sphere (since all vertices of the dodecahedron lie on the sphere's surface). Calculate the angles between all the lines (rays) that start from the center of the sphere and end to the vertices of the dodecahedron. Connect the endpoints of those lines.

or

2nd approach: Start from normal pentagons (the dodecahedron faces), calculate the angles between two adjacent faces and rotate them until you have a closed shape.

or an even more complex approach like David's (below) which uses a voronoi cell  to create the dodecahedron....

Figuring out how to implement these methods in a GH definition is, in my opinion, the second step of the exercise.

ps. of course, some of those approaches will be harder to implement than others, so it could be useful to come up with more than one and try them all out on GH in order to find the most efficient.

Permalink Reply by Kim hauer on April 2, 2015 at 5:42pm

I  concur with nikos' An understanding of the math behind any Simple Polyhedron is still fundamental to producing a wire or line 3d  representation of a solid. I would start my students with basic 2d geometry. I'm also not sure if I would use Grasshopper as my 1st choice as a programming learning experience for that task. Certainly the days of "programming "Hello my name is" needs to be replaced with more visual approach, an approach that captures the attention of students as we introduce computers and programming at younger and younger ages. After all none of those students are playing Pong on their Atari any longer. :) Its time educators get with the progam!

Permalink Reply by Judson Swets on April 3, 2015 at 12:28am

Hi Kim, most (nearly all) US geometry teachers have no knowledge of CAD and certainly not parametric modeling.  I'm working to change that in myself, and at my school.  I use a lot of Rhino, and I tell my students they can do anything.  However, when one of them comes to me and wants to model a dual snub hexpropello dodecahedron here, I know I'll need help.  This student is an exceptional learner, though.  Most students don't even think to ask that question. We've got 3 months to get it.  I hope we can get there.  

How hard of a task do you think it actually is?  

If we are completely out of our league, we will content ourselves with the platonic solids.  

With the program :), 

Judson 

Permalink Reply by David Rutten on April 3, 2015 at 3:23am

Starting with the 'pure' shape, we can worry about the planks later.

I attached a file which generates a dodecahedron, except it has a single slider which controls the elevation of the midpoints of the non-horizontal faces. You'll have to work out analytically where to put the value to get a true dodecahedron. This can be done on paper, once you understand exactly what the slider means.

Attachments:

• dodecahedron.gh, 8 KB

Permalink Reply by David Rutten on April 3, 2015 at 3:30am

And if you can't work it out, here's how to leverage the awesome power of computing and pick the best circle offset using Galapagos. It does require that you specify the fitness metric, which in this case is that all edges ought to be the same length.

Attachments:

• dodecahedron_with_solver.gh, 11 KB

Permalink Reply by David Rutten on April 3, 2015 at 3:32am

ps. If you haven't used Galapagos before, double click the pink component, switch to the second tab and press the Play button. I've set up the component to work well for this particular problem.

Permalink Reply by Judson Swets on April 3, 2015 at 1:38pm

David and Nicos, thank you.  You both have given me tons of avenues to begin exploring. I drove to school because we have macs at home, but it's 10:30 pm on a Friday night and the lab is locked.  It might be a week before I'm back with results to share.  It means a lot to me that you have taken the time to think this problem.  

Gratefully, 

Judson 

Permalink Reply by Kim hauer on April 3, 2015 at 2:31pm

I can see a huge untapped opportunity for those instructing math. A standalone Educational Mini Grasshopper. A pared down version of Grasshopper, with its own graphics display engine, not dependent on Rhino. What a tremendos classroom math tool this would be to help instruct the next generation of students in Math. ......just thinking out loud! :)

Permalink Reply by Judson Swets on April 3, 2015 at 3:44pm

Love it!  I bet motivated students from 8th grade forward could handle fully functional versions of both programs.  In my class we did a digital poster project in Rhino.  The final results are printed in color and framed.  (They look good.)  Maria found the dual snub hexpropello dodecahedron through a Google search and she wants to make it because it's complicated and pretty--that's her initial motivation.  Since I'm a novice, I reasoned that because there are so many parts, we'd be better off programming it.  (If I was wrong to think that, please tell me.)  Now we are both learning new things and that's exciting.  What I'm trying to say is that I think the next generation of math students is starting now--and it's pretty cool.  It may be a week before I can post an update.  I'll keep you in the loop.  

Judson 

Permalink Reply by Tran Huy Vu Nguyen on December 15, 2016 at 3:50pm

Hi David, can you explain me why you use the abs component ?