Game Piece

My colleague, Ms. Luna, has assigned her AP Calculus students a year-end project. They are, in groups, to create a game, based on some board game they already know, but with a Calculus theme. I enter the picture because these students imagine that they can come to me and simply say "print me something like a game piece," and I'll immediately be able to fire up my 3D printer and print out exactly the piece they are imagining. When I try to get them involved in actually designing whatever it is they want, they usually turn and walk away.

This morning I had a student, N, who was willing to work on design. (right there, it makes me happy) So we sat together and I tried to get N to give me her specifications. I tried, bit by bit, to nudge her towards speaking in terms of geometric solids.

I eventually got N to describe the game piece as a cube with a sphere sitting on top. We drafted the idea of the cube as the intersection of inequalities in the x, y, and z directions. Equation of a sphere is standard, and wasn't a problem once we decided radius and how much it should overlap the cube. From there I was able to work on designing in Mathematica.  We wound up with
RegionPlot3D[Abs[x]  < 1/2 && Abs[y] < 1/2 && Abs[z] < 1/2 || Sqrt[x^2 + y^2 + (z - 5/8)^2] < (5/8)^2, {x, -1, 1}, {y, -1, 1}, {z, -1, 2}, PlotPoints -> 50, BoxRatios -> Automatic]

I exported the plot to .stl, and opened the file in MakerWare. As usual, MakerWare wanted me to scale the drawing. She wanted two game pieces, so I copied the scaled piece a little to the right. Lately I've been printing almost everything with a raft, so I selected the raft option, reduced the solid fill to 7% (default was 10%), and clicked print.

Printing went fine. I was about to break off the raft when N stopped me. "No! I like that!" Okay by me.