Introduction

When you rotate a symmetric polygon around a mirror axis, cut the solid into two equal parts and then put the parts back together differently, you produce a sphericon.

The sphericon is a three-dimensional solid with one side and two edges. It was first introduced by the Israeli game and toy inventor David Haran Hirsch who patented it in Israel in 1980. It was given its name by Colin Roberts, of Hertfordshire, England, who also explored it. It may be constructed from a bicone (a double cone) with an apex of 90 degrees, by splitting the bicone along a plane through both apexes, rotating one of the two halves by 90 degrees, and reattaching the two halves. Generalizing this construction to a regular 2n-sided polygon (square, hexagon, octagon ...), will give access to a set of other 3D solids with the same properties as sphericons when rolling on themselves they cover their whole surface.

Fusion 360

1. Create a sketch and select a vertical plane. Then select Polygon:
   
2. Keep your radius relatively small ( to save printing time) and set the sides to an odd number:
   
3. Straighten out your polygon:
   
4. Using the Line tool, connect every other vertices:
   
   
5. Use the line tool to split your star in half:
   
6. Click trim or type t and clear all extraneous lines:
   
7. Select Revolve and rotate the profile 180°Create a sketch on the flat side and create the hole for the magnet.
   
8. Make your hole .4mm larger in diameter than your magnet (this should allow you to press fit your magnet into the model:
   
9. Export and print two.

AutoCAD

1. Create a new drawing. Select File>New Drawing:
   
2. Select acad.dwt template file and press the Open button to continue to the drawing screen.
   
3. Find the commandline.
   
   
   
   If it is not present you should be able to open it it by selecting Window> Command Line
   
   
   Other ways to display the command line are:
   • Pressing Command+3 on Mac, CTRL+9 on Windows.
   • Pressing F2
   •Typing COMMANDLINE or CLI
4. You want to set your units to millimeters. Type UN and select UN (UNITS):
   
   
   or select Format>Units from the top menu to bring up the Units Dialog box.
   
   Set your units to millimeters:
   .
5. You want to create a resolution appropriate for 3D printing. Type FACETRES and set it to 10.
6. Make sure your profiles are not deleted after you use them. Type DELOBJ. Set the value to 0.
7. In the top left corner set the Custom Visual style to Wireframe.
8. Draw a bounding rectangle and then draw a odd numbered polygon withing the boundaries:
   
9. Delete the rectangle:
   
10. Use the LINE tool to construct a star:
    
    
11. Use the LINE tool to bisect the star:
    
12. Use TRIM to trim half the star:
    
13. Turn your shape into a REGION:
    
14. Use REVOLVE to create a solid from the region. Revolve it 180°:
    
15. Change the WCS to align with the face. Use the LINE tool to find the center. Make room for a magnet:
    
16. Make sure you have a hole for your magnet that is .2mm larger in each dimension. Export and print 2.

Sketchup

Creating your regular polygon in SketchUp:

1. Open SketchUp. Use the millimeter template. Select the figure and delete it
2. Create a polygon of 5 sides:
   
3. Hold shift so that the polygon remains green and aligned with the origin:
   
4. CTRL+click on the figure and Zoom Extents:
   
5. Select the line tool:
   
6. Connect the endpoints:
   
7. Continue to connect endpoints:
   
8. Delete the excess outer lines:
   
9. Select the inner hexagon:
   
10. Delete the selection. Now draw a vertical line:
    
11. Select half the figure
    
12. Delete the selection:
    
13. Select the circle tool and change the sides to 64:
    
14. Draw a circle on the blue axis at the origin. Then select the face of the circle:
    
15. Click on the Follow Me tool and click on the half of the star:
    
    
    
16. Delete the circle:
    
17. Triple click on the form:
    
18. Select File>Export STL
    
19. Name the stl file:
    

Variations

1. Here is an eight sided polygon where the line tool connects every third endpoint:
   
2. Continue the pattern:
   
3. Continue the pattern:
   
4. Completed:
   
5. Delete half:
   
6. Add squared at each midpoint:
   
7. Continue pattern:
   
8. Delete excess outer lines:
   
9. Delete excess inner lines
   
10. Create a circle on the blue access and select the face
    
11. Click on Follow me and the face of the polygon:
    
12. Delete the circle:
    

Another variation

1. Eight sides, every endpoint connects to every other endpoint:
   

1. Here is a twelve sided polygon:
   
2. Connect every third endpoint
    
3. Continue pattern:
   
4. Or connect every fifth:
    
5. Select half:
   
6. Delete selection:
   
7. Delete excess outer and inner lines: