Very cute, and very friendly.

]]>I needed a way to get them to hold together so that I could assemble them. To do that, I left a small hole in each face. Then I got a bunch of small magnets. I used super glue to stick the magnets into the holes. If you do this, don’t glue your fingers together. You’ll feel silly. Trust me.

Of course magnets are pretty picky about which way they go together. Since most of professor Stewart’s toroids have cupolas surrounded by smaller blocks, I stuck magnets on the cupolas with the north pole facing out, and onto all the others with the south pole facing out. I did get a couple wrong though.

Once I did that, I could stick them together in various configurations from the book. Like this one, which is one of my favorites.

They’re kind of a fun toy. Here’s the latest one I’m working on.

If you’d like to print your own copy of these blocks, you can download them from my Pinshape account.

]]>The advantage of this approach is that while it might have as many quirks as a cheap pump, I’ll be able to fiddle with it when it misbehaves.

Here’s a closeup of the business end.

Hiding in there are a switch that measures the vacuum, a solenoid that controls the airflow, and a venturi that uses compressed air to generate a vacuum. That all connects up to the storage tank like this:

When the vacuum drops below the selected level, the solenoid opens and charges the venturi, which sucks more air out of the tank. It can easily maintain a vacuum of 23 or 24 inches without working too hard. It can even do 25 inches, but it’s struggling a bit at that point and the air compressor is running more than I would like. It can also hold a vacuum for an extended period of time, which is useful.

In addition to building the pump, I also installed this cool retractable hose reel yesterday.

]]>It is called the Császár polyhedron. It’s famous because it shares an interesting property with the tetrahedron. Neither of these have any diagonals! If you imagine a tetrahedron (or hold a model), you can see that if you choose any two vertices, there is an edge connecting them. This means that you can’t draw a line between them that goes through a face or the interior of the polygon.

For a long time, the tetrahedron was considered unique in this, but in 1949 Ákos Császár this second one. It has 7 vertices, 21 edges, and 14 triangular faces. As you can see, it is not convex. In fact it has a hole through the middle. You can work that out from the Euler characteristic using those three numbers. If there are any others, they’re going to have multiple holes. It’s hard to imagine any of the higher order ones being realizable, but perhaps we’ll get a surprise some day.

This is a challenging model to print, as you can see from this early attempt.

Those edges are very sharp and delicate. If you’d like to give it a try yourself, you can get the model from my Pinshape account.

]]>These are two of my favorite Kepler polyhedra:

The one on the left is called the rhombic dodecahedron. The one on the right is called the rhombic triacontahedron. They both have faces which are rhombuses. In these models, I’ve added the diagonals of the rhombuses, because they highlight their relationship to other, more familiar polyhedra.

Here’s a closer look at the dodecahedron.

The ratio of the lengths of the diagonals of these rhombuses are √2 for the dodecahedron. Although the 12 faces are identical, the vertices are not. It has 6 vertices of valence 4 and 8 vertices of valence 3. If you look closely at all of the short diagonals, you’ll notice that they’re the edges of a cube. And if you look at the long diagonals, you’ll notice that they’re the edges of an octahedron.

And here’s the triacontahedron.

The ratio of the lengths of the diagonals of these rhombuses are φ. This one has 12 vertices of valence 5 and 20 vertices of valence 3. It’s a little harder to see here, but the diagonals are again the edges of other polyhedra. The short diagonals are the edges of a dodecahedron, and the long diagonals are the edges of an icosahedron.

I printed these in the new Formlabs grey resin. If you’d like to print them yourself, you can get them from my Pinshape account here and here.

]]>Last weekend we had the annual neighborhood holiday cookie swap. As usual I was trying to decide what kind of cookies to make, and for so reason molasses cookies really appealed to me. This is based on Grandma’s Molasses Sugar Cookies, but I made a couple of changes.

Molasses Ginger Cookies

Author: Chris

Recipe type: dessert

Serves: 48 cookes

Molasses cookies with chunks of ginger.

Ingredients

- ¾ cup shortening
- ¾ cup butter
- 1¾ cup sugar
- ½ cup molasses
- 2 eggs
- 4 cups flour
- 4 tsp baking soda
- 1 heaped tsp ginger
- 2 tsp cinnamon
- 1 tsp salt
- ½-1 cup crystilized ginger, chopped into chunks

Instructions

- Melt the shortening and butter together over low heat
- While the shortening is melting sift together the flour, baking soda, ginger, cinnamon and salt in a large bowl and set aside.
- Beat the sugar together with the molasses and butter/shortening mixture with a mixer.
- Add the eggs and beat well.
- Add about a third of the flour, stir and repeat until all the flour is mixed in.
- Gently fold in the chopped ginger.
- Chill the dough for 2 hours or more.
- Preheat the oven to 350 degrees and line baking sheets with parchment paper.
- Roll the dough into balls 1.25 to 1.5 inches in diameter. Dip half in sugar and place on the trays sugar side up.
- Bake 8-10 minutes.

]]>

I could probably have fit a 1 pounder in, but I wanted the extra safety margin of a 2 1/2 pound extinguisher. They’re pretty large. I probably could have fit it under the bonnet, but that would have made it hard to get to in a hurry. Some people mount them in front of the seats, but that space is pretty precious in this car. I couldn’t have done that on the driver’s side because I need to step in that spot to squeeze under the steering wheel. It might have been possible on the passenger’s side, but that would have been pretty unfriendly for people getting a ride.

So that didn’t leave me a lot of options. I ended up attaching it to one of the rollbar stays, like this:

But even that wasn’t easy. The extinguisher I got (a nice H3R HG250) came with a quick release bracket. But that bracket is designed to attach to a flat surface. There are adapters to mount this size extinguisher to a rollbar, but most of those are designed for the heavier rollbars in a Jeep. So I made my own rollbar clamps. They look like this:

I printed them in the new Tough resin we announced the other day. That’s because you really don’t want this bracket to crack in an accident. If it did, the extinguisher would fly forward and hit the driver. This new Tough resin doesn’t crack. If it gets over-stressed, it deforms, but it doesn’t crack. And when it deforms, it absorbs a lot of energy. So it’s perfect for this job. And it looks nice too!

These rollbar clamps connect up to the quick release bracket that came with the extinguisher with a couple of M6 cap bolts. These go into nyloc nuts I embedded in the clamps.

I think the result looks pretty good!

]]>It’s hard to render because it has what are called double points. It’s also a challenging shape for a 3D printer. So today I made this:

I think it turned out pretty well. I created it with Matt Keeter’s Antimony, and then fattened up the nodes a little using Meshmixer. I used the automatic support generation in PreForm, which ended up looking like this:

It’s a really neat object. There are 65 nodes, but 15 are at infinity, so I lopped those off. Then there’s an outer shell of 20 nodes which lie on the vertices of a dodecahedron. Inside that are 30 more nodes which lie on the vertices of an icosidodecahedron. It’s really fun to hold it in your hands and rotate it around.

]]>