Designs Nobody Needs

I'm still trying to get facile with designing things for my 3D printer. I had a brief flurry of activity when I attended a workshop (thank you Math for America and Dr. George Hart). At that time I was using Mathematica, and exporting 3D plots. But my license for Mathematica expired, and I can't afford to renew it.

So I've been playing with a free tool, TinkerCAD. They have a library of some basic shapes, and if you fiddle enough with the graphic interface, you can figure out how to edit the shapes. Having attended another workshop recently where we explored Soma cube puzzles, I decided to try to make a design to print a plastic set of Soma cubes.

It's not particularly hard. Cubes are in the basic library of shapes on TinkerCAD. The only thing that took a little while to figure out is how to move an element of my design in the z-axis, since three of the basic pieces are more than one cube unit high. I made my design in two drawings: one of the four single height pieces (big L, little L, T, and Zed); and another of the three double height pieces (right chiral, left chiral, and corner).

TinkerCAD can export to .stl format, which Makerbot Desktop can open and export to .x3g for my printer. I was so proud of myself, I was about to upload the designs to thingiverse. But before doing that, I did a search. Some 48 other Soma cube designs are already up there. Nobody needs mine. But I'm happy I made it. Some day I'll even try printing it and see if it really works.

*** edit 20 Dec 2015 ***
I tried printing, and it didn't work out so good. I think my printer (Makerbot Replicator 2) may be introducing some errors in the z-axis towards the edges of the printing space. The parts more towards the center were fine, but the one furthest out had a sort of curved upper face, where it should have been completely level.

So I tweaked my designs to put just one piece per design, total of seven drawings. I'll give these a try later on today.

*** edit 22 Dec 2015 ***
My "one design per print job" drawings are printing out just fine. But I think the real problem was that the blue tape on my build plate was not sticking securely, and that introduced some waves into the build.

*** edit 5 Jan 2016 ***
An acquaintance asked for the files, so I did upload to thingiverse. Also added pictures to this post.

Soma Puzzle

Episode Three of the George Hart workshop at Math for America.

Given a supply of wooden cubes, how many shapes can you make by combining cubes such that 1) you cannot use more than four cubes, 2) rectangular prisms are not allowed, and 3) faces of cubes must match completely (no halfway or other fractional meetings). Turns out there are exactly seven different shapes.

So, if you glue the wooden cubes together into these shapes, and count them up, you have used exactly 27 cubes. By coincidence, 3^3 is 27. Can you arrange these shapes into a cube?

Yes, you can. Apparently there was a product sold decades ago called a Soma cube. It makes an interesting exploration into 3D geometric transformations. You can make the same pieces from correctly dimensioned cardboard boxes.

But you aren't limited to just a cube shape. You can make a snake, or a doggy, a dinosaur, and other shapes. Providing hours of exploration, all for a few dollars in materials.

Paper Construction from George Hart

I've been participating in a series of workshops with George Hart www.georgehart.com, and saw the activity described here at one of the workshop sessions. I tried it yesterday in one of my less-structured classes.

Overview: Students piece together twenty slotted equilateral triangles cut from card stock to make a ball. Here's what the ball looks like:

There are a few interesting things about this construction, and depending on time the facilitator can reveal these things more or less gradually. I didn't have confidence in my students' attention span, and so started on the multi-color construction.

I printed the templates on five colors of Wasau Astrobrights cardstock. Construction calls for four triangles of each color. The template prints eight to a sheet, so I precut them into halves. Students had to further cut into triangles and cut the slots. The slots are how the triangles are pieced together.

Next, students need to explore and figure out how the triangles slide together to form a stable shape. Prompts are: make a natural structure with the triangles, use the slots, structure should be three-dimensional, pieces should not be bent or folded, structure should be symmetric, and should use all twenty triangles.

Here's an example of the basic shape. Notice that five triangles combine to form a pentagonal hole.

Once students have this basic shape, it's a matter of extending around in a ball.

Once they built the ball, I then asked them to take it apart and rebuild it. This time they should make sure each pentagonal hole was surrounded by each of the five colors. About half the class was unwilling to do this. But the other half accepted the challenge and accomplished it, one staying after the bell to complete her project.

Some interesting things: A cube is visible embedded in the ball. There appear to be only four unique ways to assemble the ball with five colors to a pentagonal hole. The figure can be thought of as an icosahedron whose faces are rotated. Positioning five colors around a hole gives to opportunity to discuss permutations involving circles.