STEINMETZ SOLIDS

I designed these in fusion 360 and they are really fun to do! I believe you can do this with any regular polygon with an even number of sides (for example: squares, regular hexagons, octagons, etc.) 

The square rolls like a cylinder both backwards and forwards and side to side but not diagonals. They can roll like a cylinder in multiple ways and both of the ones posted are from identical cylinders. This means they have the same radius but different ways to turn! 
 

The hexagon is currently untested but will be tested shortly :)

PRINT AND ENJOY! :)

To design your own you first you take a cylinder with a height equal to its diameter (this cylinder looks like a perfect square in cross section).

next you pick your polygon and find its central angle (360/# of vertices) for the hexagon the central angle is 60°. so I make a axis point in the exact center of the cylinder. then you orient the other lines accordingly to form 6, 60° angles. 

then you do the “split body” or a similar function to create two opposite cross sections that look like two triangles. They should be of the center sections containing a perfect circle when viewed from above.

Then after combining them you can add any individual details you want to them. In my case I did a hole right in the middle of each piece. 

Then you go into move copy and click “create copy” you then rotate them about their center by the central angle (again for the hexagon this is 60°).  You repeat this step until you have a full shape.

Then we have to think about printability. This design on its own cannot be printed without supports but if we cut it along the right line we can print it with only a few major overhangs. I cut mine off of the highlighted line. 

Hope this was helpful! please post a comment with pictures if you design your own!

Print settings: 

• .2mm layer height
• 25% infill (gyroid)
• any material is fun!