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---
layout: post
title: 'Three cylinders: random geometry geekery'
permalink: '/three_cylinders/'
tags: ['math', '3d objects']
---
<p>
The intersection of three cylinders (and six half-cylinders) are interesting
objects and make for fun random desk objects. They are also fun to build out
of wood (takes some time) or 3D print (mostly trivial).
</p>
<p>
The intersection of three cylinder at a right angle results in a
Steinmetz solid. Calculating the volume of the intersection is a classic
math puzzle.
</p>
<img src="/files/2015/three_cylinders/three_cylinders.gif">
<small>(image courtesy of Van Helsing)</small>
<p>I made a virtual 3d model that you can interact with in <a href="http://openjscad.org/#http://quaxio.com/files/2015/three_cylinders/three_cylinders.jscad">openjscad</a>.</p>
<p>
The intersection of six cylinders results in a cube, which can seem counter
intuitive at first given that cylinders are curved objects.
</p>
<img src="/files/2015/three_cylinders/six_cylinders.jpg">
<p>You can also play with this case in <a href="http://openjscad.org/#http://quaxio.com/files/2015/three_cylinders/six_cylinders.jscad">openjscad</a>.</p>
<p>If you like interesting geometric shapes, make sure to checkout <a href="http://www.shapeways.com/designer/mehtikruton3ddesign?li=pb">mehtikruton's online store</a>, full of fun 3d printed objects! <a href="http://hof.povray.org/Riemann_Sphere-Isosurface.html">Loxodrome Spirals</a> are fun
to look at too.</p>