Constructing a shape as near to a sphere as possible

[Soapyjoe]

Hi,

I have previously asked about this problem so I do apologize.

What I wish to do is place around a Dodecahedron twelve (one for each side) profiled parts that will convert the dodecahedron into a sphere.

My idea is to encase a previously modelled dodecahedron with clear Perspex ... then flame treat it so that I end with the dodecahedron in a sort of crystal ball.

Soapy

[4DThinker]

How big is one side of your dodecahedron?

[4DThinker]

According to Google the dihedral angle between faces is 116.57 degrees. Half of that (58.285 degrees) would be the miter angle at the edge of each pentagon. For a 3 inch radius pentagon face a little drafting told me a sphere to cover the dodecahedron would need to be 9.8839 in diameter. The thickness of plex would need to be 1.015 inches to cut a section of the sphere. Using a 2-sided job, and a 1.015 inch tall half section of the sphere perimeter I cut the curve top. On the 2nd side I used the pentagon outline and a drawing of the miter angle to cut the mitered faces on the edges. Aspire versions 9.519 file attached. Scale to fit your desired size.

4D

[Soapyjoe]

Hi,
Thanks.
The length of one side of my pentagons are 70mm
Soapy

[4DThinker]

For a 70mm sided pentagon I ended up using 20.42mm thick material close to 120mm square to cut one sphere section. A 2-sided job and a moulding toolpath for both the spherical side and the mitered edge side. You might cut one out of MDF or dense foam to verify size.

Hope it works out. Post a photo once you are done if it does.

[Soapyjoe]

Hi,

I am sorry 4DThinker but your attachment refuses to open-up on my copy of the Vectric software (10.021)

Could we perhaps simplify the task by considering converting a cube into a sphere by placing appropriate shaped pieces onto each of the six faces.

What I would really appreciate is for guidance (in perhaps baby-steps) of a method of producing the above components.

Soapy

[4DThinker]

Odd. Typically in the past newer versions would open files from older version but not the other way around. You aren't by chance using a trial version are you? Or perhaps a desktop version might be the conflict.

The best I can do is post a .DXF you should be able to import/open. I added a bit of text to label the assorted vectors used.
I learned drafting 40 or so years ago and have been playing with CNCs for 7 or 8 years now using Aspire for most of them. Not sure I can just explain what I did if you haven't had similar experiences.

4D

[Tailmaker]

Hi,

I am sorry 4DThinker but your attachment refuses to open-up on my copy of the Vectric software (10.021)

I can open it just fine with new version Aspire. It complains about an invalid vector but opens anyway.
Are you trying to open with VcarvePro?

4D's method with the molding tool paths is pretty straight forward. But you would have to cut the side chamfers first, flip and clamp on the inside flat (probably best with a vac pod or double sided tape against a removable fence) and then cut the sphere from the other side.
I would also not let the corners get to zero thickness or you will melt them away with the torch when polishing.

[Soapyjoe]

Thanks,
In the end I did manage to get the file to download... with the message about some fault.
I have decided to make a trial , first in hardwood cutting the half dihedral angles with the chamfer tool then reversing the workpiece, accurately centring then shaping the curved surface,
The tip about fine edges melting away is well worth noting.
Thanks again.
Soapy

[4DThinker]

I can open it just fine with new version Aspire. It complains about an invalid vector but opens anyway.

I noticed when selecting all the vectors that an odd vector appeared that I hadn't drawn. It didn't show when nothing was selected, and I couldn't isolate/select it no matter how I tried. I'm going to have to call it a ghost vector, and possibly a flaw in Aspire. It ran from the bottom corner of the screen up to a point in the globe circle I drew. When I zoom in or out or pan around the line stays attached to the bottom left corner of the 2D view, and actually changes angle on the screen.

First time and possibly last time I'll ever come across such a thing in Aspire.

As to the possibility of melting the thin end, it is only a knife point at the corners of the pentagons. If you want to add some thickness there a larger diameter circle to change the sphere moulding vector, a slight change to the chamfer vector, and thicker material would yield a sphere section with no thin or knife edges.

4D

[4DThinker]

Took about 5 minutes to revise the file so the corners wouldn't come down to a sharp point. Thicker material required (24.095mm) and a larger resulting sphere (205.32mm diameter), but might work better if flame smoothing. Let me know if this file still generates an error when opening. I found a way to get just the ghost vector selected, then hit the delete key to get rid of it.

4D

[Tailmaker]

SoapyJoe and 4D-Thinker, if you are really into polyhedra, you can check out my AnyMiter app to cut the faces. It has a pretty good selection of common ones. I never published the program and used it only myself (I guess the market would be really small...) but it is pretty slick for this specific purpose. Oh, and the download has no user instructions but I hope it is rather self explanatory. Manuals are boring, anyway
https://www.dropbox.com/s/3ypdbyv7ixztp ... n.zip?dl=0
Just unzip anywhere and run the .exe (no virus except COVID 19).

[4DThinker]

Nice of you to offer the app Tailmaker. I'm going to resist the temptation to try it out though as in this day of social isolation some of my anti-boredom activities include jigsaw puzzles and figuring out how to do things I've never done before. I wasn't sure I could figure out SoapyJoe's request but enjoyed trying to do it anyway. I'm 62 and have personally never bumped into a need for complex solid shapes other than cubes and cylinders on a few occasions. None have needed spheres they would fit inside of. A nice mental challenge though.

4D

[4DThinker]

I don't know how far you are along, SoapyJoe, but I just finished cutting out 12 sections with pentagons that were 2" on a side. I used 3/4" thick scraps of red oak and hickory I had in my shop. After taping them all up I had something danged close to a perfect sphere.

Now I'm contemplating how best to glue them up. Thinking about making 2 halves so the globe can be opened to see the interior pentagon faces. Maybe a few small rare earth magnets to stick the sides together. A bit curious about having used hardwood given it may expand or shrink across the grain. As far as I can tell there is no way to glue up all the pieces so each glued edge is two pieces with the same relative grain edge mating up. A consequence of 5 sides no doubt.

4D

[4DThinker]

My toolpath test. It took a few tries to master cutting one face out without and flaws. The inside chamfers were easy, but holding down the pieces to cut the spherical face was the challenge. I've got "almost" a perfect wood ball. Two halves that each look good but don't quite meet up on all chamfered edges. This test does prove that the chamfer tool paths are correct to make a sphere though.

4D