## Saturday, March 30, 2013

### Monostatic Body

I received the 3D print of the one-sided die that I designed. Unfortunately it sometimes gets stuck upside-down on the unstable equilibrium. I have designed a new version which I think should fix the problem: http://www.shapeways.com/model/979729/monostatic-body.html. This version has a ridge on top which should make the unstable equilibrium... less stable:

The ridge causes the center of mass to raise a bit (to 0.9mm below the cylinder's center). I feel confident that this version of the shape should work - it will take about two weeks until I get the printed copy from Shapeways.

## Sunday, March 17, 2013

### One-sided die

Today I designed a one-sided die: http://www.shapeways.com/model/979729/one-sided-die.html

I have ordered a 3D print of the model.

A sphere does not make a very good one-sided die because it takes a long time to stabilize after rolling. The shape I designed has some interesting properties. It has only one stable equilibrium, so it will always rest in the same position on a flat surface. It is also homogeneous and convex. A gömböc is another shape with these properties. Unlike a gömböc, my shape has multiple unstable equilibrium points.

My shape is similar to a monostatic polytope described in 1969 by J.H. Conway, M. Goldberg and R.K. Guy. Here is a video demonstrating their shape:

Unlike Conway's shape, my design is smooth everywhere except a flat surface on the bottom. I added the flat surface to help it stabilize faster. It is actually very easy to construct my shape - it is the intersection of a sphere with a cylinder (ignoring the flat bottom). For the design I uploaded to Shapeways, the cylinder has a radius of 10mm and the sphere has a radius of 30mm. It was modeled using Rhino:

The highlighted point in the screenshot is the center of mass - it is 1.059mm below the cylinder's center. I am hoping that the center of mass is low enough so that the actual physical object always reaches the same resting point. Theoretically any center of mass below the cyclinder's center would work, but in practice inaccuracies in the 3D printing process could cause problems.

## Friday, March 15, 2013

### Gyroid

I ordered a 3D print of a gyroid from Shapeways. The material is alumide. I am very impressed with the quality of the print - I plan to create some of my own models soon.