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My adventures in 3D printing: Prime number sieve

At work we’ve got a 3D printer. In this series of posts I’ll share some of the designs I’ve made.

Hand holding a stack of 3D printed squares, with holes cut out.

This is something I’ve wanted to make for a long time: a literal sieve of Eratosthenes.

This is a collection of trays which stack on top of each other.

Each tray has a grid of holes, with some holes filled in. The tray with a “2” on it has every second hole filled in; the tray with a “3” has every third hole filled in; and so on.

Four trays, corresponding to numbers 2,3,4 and 5

When the trays are stacked together, the holes you can see through correspond to prime numbers: every other number is filled in on one of the trays.

I went through quite a few iterations of this design. The first version was a series of nesting trays. After printing it, I realised that you might want to put the trays in a different order. After that, I did a lot of fiddling with different ways of making the plates stack on top of each other. The final version has sticky-outy pegs at each corner, and corresponding holes on the other side. I had to add a fair bit of margin around the holes so the wall didn’t go wiggly when printed.

You can download .scad and .stl files for the prime number sieve at Thingiverse.

My adventures in 3D printing: Wallis’ Sheldonian theatre roof

At work we’ve got a 3D printer. In this series of posts I’ll share some of the designs I’ve made.

Several dozen black beams woven together to make a single structure, supported only at the edges.

The roof of the Sheldonian theatre in Oxford, built from 1664 to 1669, is constructed from timber beams which are unsupported apart from at the walls, and held together only by gravity.

My adventures in 3D printing: Spherical pseudo-cuboctahedron

At work we’ve got a 3D printer. In this series of posts I’ll share some of the designs I’ve made.

This shape is a “spherical pseudo-cuboctahedron”, prompted by a request from Jim Propp on the math-fun mailing list.

3D printed sphere with edges cut out of it, making squares and triangles which meet halfway along the edges

It has 24 vertices, 12 edges and 14 faces. That doesn’t satisfy Euler’s formula $V – E + F = 2$, so it can’t be a proper polyhedron – hence “pseudo-cuboctahedron”.

However, if you push all the vertices onto the surface of a sphere, all the edges are spherical arcs, it sort of works.

While designing this object, I got fed up with OpenSCAD‘s awkward control syntax, and switched to Python. I wrote Python code to produce the coordinates of points along the edges, which the SolidPython library turned into something that OpenSCAD can cut out of a sphere.

You can download all the files needed to print your own spherical pseudo-cuboctahedron from Thingiverse.

My adventures in 3D printing: Write Angles Cube

At work we’ve got a 3D printer. In this series of posts I’ll share some of the designs I’ve made.

Three whiteboard stuck in the write angles cube at right angles.

This is one of the first ‘proper’ things I’ve designed – I wanted to have a go at making something based on an object I already had. A colleague asked if I could make some props to explain coordinate systems, and I was holding a whiteboard pen at the time, so I decided to make a set of orthogonal axes out of whiteboard pens.

Make your own bauble with icosahedral symmetry with Shapeways

shapeways-bauble

Internet 3D printing emporium Shapeways has released a nifty little tool to create your own unique Christmas bauble, which they’ll print out and send to you in time for the festive season.

It works by mapping a triangular design onto a blown-out icosahedron, and applying some “kaleidoscope effects”. As far as I can tell, that means they expand and rotate the patterns so they overlap.

There’s a selection of built-in patterns you can choose from, or you can upload your own pattern to make a really unique decoration. However, because the resulting object needs to exist in the real world, you need to take care to make sure it all comes out in one connected piece. Shapeways have written some very clear instructions about how to achieve that.

Play: Ornament Creator from Shapeways

via Vladimir Bulatov on Google+, who seems to work for Shapeways now. Exciting!

Vi Hart has 3D printed a hypercube made of monkeys that has the symmetries of the Quaternion group

Group theorists, often interested principally in the abstract, have been known to neglect the vital importance of producing funky gizmos that exhibit the symmetries they have theorized about. Internet maths celeb Vi Hart, working with mathematician Henry Segerman, has addressed this absence in the case of $Q_8$, the quaternion group. The object they’ve designed is four-dimensional and made of monkeys, and they’ve done the closest thing possible to making one, which is to 3D-print an embedding of it into our three-dimensional universe, also made of monkeys. Their ArXiv preprint (pdf) is well worth a read, and when you get to the photos of the resulting sculpture (entitled “More fun than a hypercube of monkeys”), you’ll fall off your chair.

Further reading

The Quaternion Group as a Symmetry Group by Vi Hart and Henry Segerman, on the ArXiv.

Nothing Is More Fun than a Hypercube of Monkeys at Roots of Unity, including an animated gif of a virtual version of the sculpture rotating through 4D-space.

Henry Segerman’s homepage

Vi Hart’s home page

Google+