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A "sphericon" is a pleasing 3-dimensional shape formed by joining four half-cones. It is a "developable" shape, meaning that all parts of it touch a flat surface it is rolled on, and it has an interesting wobbly motion when it rolls. We'll make the shape by halves, in Autodesk Inventor.

Step 1: Making the Half-Shape


To make the first half, we will make a half-square one inch on the sides. Do this in a 2-D Sketch as shown. The diagonal will be used as the axis of rotation.

Step 2: Making the Solid of Revolution

Next let's make a solid of revolution from the half square, as shown, by using the Revolve 3D command. Revolve the triangle 180 degrees with the hypotenuse as the axis. You can think of this solid as two half-cones mated at the base.

Step 3: Mate the Two Halves

Make the other half by copying the solid you just Revolved. Note that both sides have a square base. If you mated the square base with the apexes matching, you would get two cones (a "bicone") joined at their base. But here's the twist: to make a sphericon, rotate one of the halves 90 degrees with respect to the other, so the apexes met the base edges. Then mate the two halves by Constraining two of the square edges to be coincident.

Step 4: Printing and Polishing

This turned out to be an easy print on the Objet stereolithography printers at Pier 9. I used the Vero clear resin, and polished it. I started with the polishing instructions from Robb and Noah, but since I am a little lazy, I skipped a lot of the grit and the steps. I started with 320 grit sandpaper, then went directly to a wet sand with 1000 grit. I missed a few spots and had to touch up with the 320 grit again, but NBD. After that I went directly to the buffing wheel. Perhaps not optically perfect but it looks fine to me, and it took perhaps 30 minutes.

Step 5:

Here's another version with smoothed edges in case anybody cares ;)

<p>This looks good so I wanted to see what it looked like moving. There's a good video of two here, one like this (order 2) and one of order 4:</p><p><iframe allowfullscreen="" frameborder="0" height="281" src="//www.youtube.com/embed/8OgA3UW9Adc" width="500"></iframe></p><p>The one of order 4 looks even more interesting and has a freaky, has it stopped or not, motion.</p>
<p>Just stumbled upon this one. Very cool! The motion of the second one is really quite animated. How was the order 4 sphericon generated? And would you be able to share your STL or OBJ file? Thanks!</p>
<p>I only found the video, I was not the maker<br> of them. However, going back to the original YouTube video, they <br>referenced here for details of the sphericon:</p><p><a href="http://www.thingiverse.com/thing:112367" rel="nofollow">http://www.thingiverse.com/thing:112367</a></p><p>It also led to this, a singing oloid, which I found quite hypnotic:</p><p>http://www.youtube.com/watch?v=2d2RchtzD-4</p>
<p>Here is a pic of the shericon I made after I decided the standard could look better.<br>And a little video of it in motion:</p><p><iframe allowfullscreen="" frameborder="0" height="281" src="//www.youtube.com/embed/L41pP1f_x6E" width="500"></iframe></p>
<p>This is cool, would you mind if I used a video of it rolling at the end of the video I am making for my <a href="https://www.instructables.com/id/Chimera-60-DLP-resin-3d-printer/" rel="nofollow">$60 3D printer?</a></p>
this shape is intriguing... I want to try it. maybe after I make the $60 DLP 3d printer(sorta recent instructable)
<p>I'll try to print one out and see how it works.</p>
<p>Now you really made me want a DLP printer....<br>Currently into a 14H print but after that I have to try this thing.<br>I guess my cats will go mental on it :)</p>
Very interesting! We studied these in my calculus class but I never imagined one would roll so interestingly.<br><br>Have a great day!
<p>Awesome!</p>

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