A member on Vectric's forum wanted to know how to cover a flat faced dodecahedron (12 sided solid) with a sphere. He plans to cut the sections from acrylic to end up with a transparent spherical ball that you can see the dodecahedron faces within.  I was able to figure out the CNC cuts needed, but in these days of isolation thought it would be a useful distraction to verify my solution.    I cut each section from scraps of red oak and hickory I was able to scrounge from assorted places in my garage shop.  3/4" thick exactly over pentagons that were 2" on a side.    It took a couple of tries to find a cutting strategy that worked, and a few of the sections show scars from early mistakes.  Right now I have two glued-up halves.  One is made from perfect sections and all seams meet perfectly.   The other half has sections with chips missing and scars from work slipping while being cut.   Not worth gluing together right now, but I though I'd share the work to date.   I don't really need a wood soccer ball so may end this experiment here.  It did verify that my calculations were correct for how to toolpath sphere sections to cover a dodecahedron.   Cutting them out was another challenge altogether!

 

In the first photo you can see a short dowel on the left side, sticking up from the bed of my CNC.  Each section has a 1/4" hole cut in the center of the pentagon inside.  I cut the chamfered edges and center hole first, then flipped the wood over and impaled it over the dowel to cut the spherical side.  A drop of wood glue on a corner kept the pieces down and prevented turning around the dowel.  Moulding toolpaths on both sides. 

 

4D  

 

 

That took some work, and some serious brain activity.  Heck I was hemorrhaging brain cells in the first  two sentences.  

1 hour ago, 4DThinker said:

flat faced dodecahedron

 

 

1 hour ago, 4DThinker said:

He plans to cut the sections from acrylic to end up with a transparent spherical ball that you can see the dodecahedron faces within.

In a couple of other threads the author of the original inquiry posted photos of dodecahedrons he'd been making.   Each face had a different carving on it.   Something interesting to see on each face.  In one case it was a different religious symbol on each.   As I was carving the wood sections I had a momentary thought of VCarving the name of each month on the different faces.  Maybe make a nice wood base for it so I can put the green tape back in service.   I'll likely sand everything smooth and put some tung oil on them, then add the sphere to the collection of CNC samples I have in the university fab lab where I work (when there is no pandemic going on). 

 

4D  

Edited April 19, 20206 yr by 4DThinker

An interesting project 4D, thanks for sharing with us.  Post up more pics after the finish is applied.  And for sure, the transparent ball when it's done.

Thanks Cal,

 

I'm not making the acrylic version.   The fellow who made the dodecahedron with religious symbols on each face is.  I'll post a link to the Vectric forum when and if he ever posts a photo of the clear version. 

Over there every now and then someone will ask for strategies on how to CNC cut a sphere.  Various reasons, from wanting to make Christmas tree ornaments to Croquet balls to 3D surface models of the earth or moon. Not sure this strategy would apply well to any of those, but it definitely is one way to cover a dodecahedron with a sphere.  I previously helped the same fellow make toolpaths for sphere sections to cover a cube, but never cut them myself. 

 

4D

That is so neat and I love the way you went about cutting it!

27 minutes ago, John Moody said:

That is so neat and I love the way you went about cutting it!

Thanks John.   I've got a 3D printer and some wood-filled PLA filament for it.  Since you can turn toolpath previews into 3D models using Aspire, then export them I might make a smaller scale version using the 3D printer.  

 

4D