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</article>
<article>
<h2>Latest gomepost</h2>
<a class='journal-link' href='journal/wardrobe.html'>
<h3>Wardrobe updates</h3>
<div class='line stop-4'></div>
<time datetime='Tue, 31 Jan 2023 11:00:00 CST'>31 Jan. 2023, 11:00 PM</time>
<p>I have no idea what I’m talking about when it comes to fashion</p>
<a class='journal-link' href='journal/rhombic-dodecahedron.html'>
<h3>Tesselating building units in Minecraft</h3>
<div class='line stop-3'></div>
<time datetime='Wed, 1 Feb 2023 11:00:00 CST'>1 Feb 2023, 11:00 PM</time>
<p>A signature of my Minecraft building style</p>
</a>
</article>
<article id='listening'>

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<main>
<h1>Journal</h1>
<a href='rss/feed.xml' class='rss-link'>RSS feed</a>
<a class='journal-link' href='rhombic-dodecahedron.html'>
<h3>Tesselating building units in Minecraft</h3>
<div class='line stop-3'></div>
<time datetime='Wed, 1 Feb 2023 11:00:00 CST'>1 Feb 2023, 11:00 PM</time>
<p>A signature of my Minecraft building style</p>
</a>
<a class='journal-link' href='wardrobe.html'>
<h3>Wardrobe updates</h3>
<div class='line stop-4'></div>

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<!DOCTYPE html>
<html lang='en'>
<head>
<title>gome — rhombic dodecahedron</title>
<meta charset='utf-8'/>
<meta name='theme-color' content='#efe5d7'>
<meta name='viewport' content='width=device-width, initial-scale=1.0, shrink-to-fit=no'/>
<link rel='icon' type='image/x-icon' href='../favicon.ico'>
<link rel='preconnect' href='https://fonts.googleapis.com'>
<link rel='preconnect' href='https://fonts.gstatic.com' crossorigin>
<link href='https://fonts.googleapis.com/css2?family=Lora:ital@0;1&display=swap' rel='stylesheet'>
<link rel='stylesheet' type='text/css' href='../css/style.css'/>
</head>
<body>
<header id='header'>
<nav>
<a href='..'>back to gomepage</a>&mdash;<a href='.'>journal</a>
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<main>
<article>
<h1 id='title'>Tessellating building units in Minecraft</h1>
<time datetime='Wed, 1 Feb 2023 11:00:00 CST'>1 Feb 2023, 11:00 PM</time>
<p>
Geometry is one of those subjects that’s a ton of fun to read about on Wikipedia.
With most other mathematical subjects, the material is so in-depth that most of it goes above the head of a layperson.
That’s also true with geometry, but at least there are fun pictures to look at.
</p><p>
One of my favorite shapes I ever discovered on Wikipedia is the <a href='https://en.wikipedia.org/wiki/Rhombic_dodecahedron' target='_blank'>rhombic dodecahedron</a>.
Twelve was my favorite number as a kid, and it has twelve faces.
The faces are all identical but not made of regular polygons, which I believe makes it unique among convex polyhedra (but I’m not 100% sure on that).
It has a satisfying level of complexity but it’s easily recognizable.
And best of all, it tessellates in three dimensions.
</p>
<figure>
<img src='https://upload.wikimedia.org/wikipedia/commons/thumb/d/d9/Rhombic_dodecahedra.png/480px-Rhombic_dodecahedra.png' width='480' height='480' class='no-border' />
<figcaption>Image credit: <a href='https://commons.wikimedia.org/wiki/File:Rhombic_dodecahedra.png#Licensing' target='_blank'>Andrew Kepert</a></figcaption>
</figure>
<p>
At some point when playing Minecraft, I had the idea to try building using repeating tessellating units.
The rhombic dodecahedron was a perfect candidate, because it tessellates in line with a cubic grid, which is the whole basis of Minecraft.
It’s actually a very closely related shape to a cube, because you can create one from a cube by popping its faces out into pyramids.
</p>
<figure>
<img src='https://upload.wikimedia.org/wikipedia/commons/5/50/R1-cube.gif' width='240' height='240' />
<figcaption>Image credit: <a href='https://commons.wikimedia.org/wiki/File:R1-cube.gif#Licensing' target='_blank'>TED-43</a></figcaption>
</figure>
<p>
So I went into Minecraft and built out a few examples, trying to get a version of the shape with a good relative size and ease of building.
I settled on a slightly modified design that looks like this:
</p>
<figure>
<img src='img/rhodo_single.webp' width='400' height='400' />
<figcaption>The cubic frame is in red & white to show the side length of five, while the popped out faces are in yellow.</figcaption>
</figure>
<p>
The faces don’t terminate in points, because in Minecraft it would just end up being a single block floating there on each face, and that didn’t look very good.
This is what three of them tessellating together looks like:
</p>
<figure>
<img src='img/rhodo_triple.webp' width='400' height='400' />
<figcaption>You can just keep extending the frame of 5×5 cubes and building the appropriate yellow faces where needed.</figcaption>
</figure>
<p>
I love the look of these units.
They take advantage of Minecraft’s classic blocky look while including some rounding, so they don’t feel utterly boxy.
They’re versatile and well-sized for building a useful room.
Also, they are pretty easy to modify or augment as needed, so they make a great starting point for a new build.
</p>
<figure>
<img src='img/rhodo_home.webp' width='600' height='600' />
<figcaption>A quick example home I threw together to demonstrate how the units can be built into the landscape nicely</figcaption>
</figure>
<p>
I came up with these units years ago, but I keep coming back to them whenever I want to play Minecraft again.
Because they’re so simple, it’s easy to try a lot of new things with them, and I never run out of ideas for new ways to use them.
But despite their simplicity, they’re distinctive and (as far as I know) unique to me, so I consider them a signature of my Minecraft building style.
</p><p>
Do you play Minecraft?
Do you have any signature building patterns or techniques?
Do you like to read about geometry on Wikipedia?
Let me know your thoughts at my Ctrl-C email: <code>gome<span style='user-select: none;'>&nbsp;&#8203;</span>@<span style='user-select: none;'>&nbsp;&#8203;</span>ctrl-c.club</code>.
</p>
</article>
</main>
</body>
</html>

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