writing challenge 47/100
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color: #323a42;
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font-family: 'Palatino Linotype', serif;
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font-family: 'Palatino Linotype', Lora, serif;
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font-family: Optima, 'Palatino Linotype', sans-serif;
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font-family: Optima, 'Palatino Linotype', Lora, sans-serif;
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a.journal-link h3 {
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font-family: 'Palatino Linotype', serif;
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font-family: 'Palatino Linotype', Lora, serif;
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html {
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color: #323a42;
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background-color: #efe5d7;
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font-family: 'Palatino Linotype', serif;
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font-family: 'Palatino Linotype', Lora, serif;
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h2, h3, ul, ol, p, main img {
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10
index.html
10
index.html
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@ -59,11 +59,11 @@
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</article>
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<article>
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<h2>Latest gomepost</h2>
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<a class='journal-link' href='disagreeing.html'>
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<h3>Disagreeing with friends</h3>
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<div class='line stop-2'></div>
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<time datetime='Thu, 2 Feb 2023 11:30:00 CST'>2 Feb 2023, 11:30 PM</time>
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<p>It’s precisely those sites of disagreement where we build trust that our friendship can transcend our differences.</p>
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<a class='journal-link' href='journal/worst-shape.html'>
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<h3>Quest for the worst shape</h3>
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<div class='line stop-1'></div>
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<time datetime='Fri, 3 Feb 2023 11:30:00 CST'>3 Feb 2023, 11:30 PM</time>
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<p>Why are we paying mathematicians to come up with these atrocities?</p>
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</a>
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</article>
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<article id='listening'>
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<main>
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<h1>Journal</h1>
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<a href='rss/feed.xml' class='rss-link'>RSS feed</a>
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<a class='journal-link' href='worst-shape.html'>
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<h3>Quest for the worst shape</h3>
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<div class='line stop-1'></div>
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<time datetime='Fri, 3 Feb 2023 11:30:00 CST'>3 Feb 2023, 11:30 PM</time>
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<p>Why are we paying mathematicians to come up with these atrocities?</p>
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</a>
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<a class='journal-link' href='disagreeing.html'>
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<h3>Disagreeing with friends</h3>
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<div class='line stop-2'></div>
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@ -81,6 +81,14 @@
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Do you like to read about geometry on Wikipedia?
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Let me know your thoughts at my Ctrl-C email: <code>gome<span style='user-select: none;'> ​</span>@<span style='user-select: none;'> ​</span>ctrl-c.club</code>.
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</p>
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<figure>
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<img src='https://upload.wikimedia.org/wikipedia/commons/9/90/Cubes-R1_ani.gif' width='450' height='450' />
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<figcaption>
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Bonus image: I stumbled on this while writing Friday’s post.
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It’s a much better demonstration of how rhombic dodecahedra tessellate, so I thought I’d include it here after the fact.<br/>
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Image credit: <a href='https://commons.wikimedia.org/wiki/File:Cubes-R1_ani.gif#Licensing' target='_blank'>TED-43</a>
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<width>144</width>
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</image>
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<item>
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<title>Quest for the worst shape</title>
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<author>gome</author>
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<pubDate>Fri, 3 Feb 2023 11:30:00 CST</pubDate>
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<link>https://ctrl-c.club/~gome/journal/worst-shape.html</link>
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<guid>https://ctrl-c.club/~gome/journal/worst-shape.html</guid>
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<description>Why are we paying mathematicians to come up with these atrocities?</description>
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<enclosure url="https://ctrl-c.club/~gome/journal/img/600-cell_net.webp" length="62638" type="image/webp" />
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</item>
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<item>
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<title>Disagreeing with friends</title>
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<author>gome</author>
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<!DOCTYPE html>
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<html lang='en'>
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<head>
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<title>gome — worst shape</title>
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<meta charset='utf-8'/>
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<meta name='theme-color' content='#efe5d7'>
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<link rel='icon' type='image/x-icon' href='../favicon.ico'>
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<link rel='preconnect' href='https://fonts.googleapis.com'>
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<link rel='preconnect' href='https://fonts.gstatic.com' crossorigin>
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<link href='https://fonts.googleapis.com/css2?family=Lora:ital@0;1&display=swap' rel='stylesheet'>
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<link rel='stylesheet' type='text/css' href='../css/style.css'/>
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</head>
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<body>
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<header id='header'>
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<nav>
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<a href='..'>back to gomepage</a>—<a href='.'>journal</a>
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</nav>
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</header>
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<main>
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<article>
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<h1 id='title'>Quest for the worst shape</h1>
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<time datetime='Fri, 3 Feb 2023 11:30:00 CST'>3 Feb 2023, 11:30 PM</time>
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<p>
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In <a href='rhombic-dodecahedron.html'>Wednesday’s post</a>, I wrote that I enjoy learning about geometry on Wikipedia,
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and about a very nice shape that I found there, the rhombic dodecahedron.
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Another thing I enjoy doing from time to time is hunting for the most messed-up, the most wicked, the most cursed shapes possible.
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So let’s explore some of the worst shapes I’ve found together.
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</p>
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<h3>Great grand stellated polydodecahedron</h3>
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<figure>
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<img src='https://upload.wikimedia.org/wikipedia/commons/thumb/3/34/Ortho_solid_016-uniform_polychoron_p33-t0.png/480px-Ortho_solid_016-uniform_polychoron_p33-t0.png' width='480' height='480' />
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<figcaption>Image credit: <a href='https://www.software3d.com/Stella.php' target='_blank'>Robert Webb’s Stella</a></figcaption>
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</figure>
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<p>
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We’re starting things off gently with a not-so-terrible shape.
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This is a 4-dimensional polytope made of 120 great stellated dodecahedra (a self-intersecting dodecahedron with pentagrams for faces).
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This one might give you a start if you bumped into it around a blind corner, but it’s more intimidating than truly depraved.
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Once you get to know it, you might even regard it as beautiful in its own way.
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</p>
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<h3>5-orthoplex</h3>
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<figure>
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<img src='https://upload.wikimedia.org/wikipedia/commons/5/56/Pentacross_wire.png' width='480' height='480' />
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<figcaption>Image credit: <a href='https://commons.wikimedia.org/wiki/File:Pentacross_wire.png#Licensing' target='_blank'>Claudio Rocchini</a></figcaption>
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</figure>
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<p>
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The 5-orthoplex is not such a bad shape on its own.
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It’s actually a fairly simple 5-dimensional shape, being the dual of the 5-cube.
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It consists of 32 4-simplexes (the 4D extension of a triangle).
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</p><p>
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What makes this incarnation of it so truly awful is its tortured journey into our 3-dimensional world, not to mention the further bondage it endures to fit on your 2D screen.
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To put it simply, this is a perspective projection of a stereographic projection of a Schlegel diagram of the 5-orthoplex.
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I’ll spare you the gory details, but essentially, this shape has been put through a lot, and now it’s hungry for revenge.
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</p>
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<h3>600-cell, <span style='font-variant: small-caps;'>aka</span> hexacosichoron, hexacosihedroid, tetraplex, polytetrahedron, or C<sub>600</sub></h3>
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<figure>
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<img src='https://upload.wikimedia.org/wikipedia/commons/thumb/9/9a/600-cell_net.png/524px-600-cell_net.png' width='524' height='480' />
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<figcaption>Image credit: <a href='https://www.software3d.com/Stella.php' target='_blank'>Robert Webb’s Stella</a></figcaption>
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</figure>
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<p>
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We’re back down to four dimensions again, but this one brings a lot of cells to the table, as well as some freaky images.
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This first one is the net of the 600-cell, which means it’s unwrapped to display the writhing mass of tetrahedra that make it up.
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Here’s an projection of it rotating:
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</p>
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<figure>
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<img src='https://upload.wikimedia.org/wikipedia/commons/1/1e/600-cell.gif' width='255' height='255' />
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<figcaption>Look at it seethe.<br/>Image credit: <a href='https://commons.wikimedia.org/wiki/File:600-cell.gif#Licensing' target='_blank'>Jason Hise</a></figcaption>
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</figure>
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<p>
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And to top it off, here it is forced through an unseemly chain of projections like the 5-orthoplex:
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</p>
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<figure>
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<img src='https://upload.wikimedia.org/wikipedia/commons/thumb/4/43/Stereographic_polytope_600cell.png/480px-Stereographic_polytope_600cell.png' width='255' height='255' class='no-border' />
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<figcaption>There’s way too much going on in the center of this image.<br/>Image credit: <a href='https://commons.wikimedia.org/wiki/File:Stereographic_polytope_600cell.png#Licensing' target='_blank'>Althepal</a></figcaption>
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</figure>
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<h3>Crossed square antiprism</h3>
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<figure>
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<img src='https://upload.wikimedia.org/wikipedia/commons/5/52/Crossed_square_antiprism.png' width='360' height='403' class='no-border' />
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<figcaption>Image credit: <a href='https://commons.wikimedia.org/wiki/File:Crossed_square_antiprism.png#Licensing' target='_blank'>Tomruen</a></figcaption>
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</figure>
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<p>
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The simplest shape we’ve seen so far, but simply demented.
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Why would you make a shape like that?
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</p>
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<h3>Boy’s Surface</h3>
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<figure>
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<img src='https://upload.wikimedia.org/wikipedia/commons/b/bb/Boy_Surface-animation-small.gif' width='400' height='400' />
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<figcaption>Image credit: <a href='https://commons.wikimedia.org/wiki/File:Boy_Surface-animation-small.gif#Licensing' target='_blank'>A13ean</a></figcaption>
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</figure>
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<p>
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This one gets points for the funny name alone.
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This is the first non-polytope of the batch; it’s actually a result from topology.
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Werner Boy was told by his teacher David Hilbert to prove that projective plane could <b>not</b> be immersed in 3D space.
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Instead, he ended up finding a way to do it, and this goofy shape is the result.
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Strange and lumpy in all the wrong places, Boy’s Surface is more unpleasant and comedic than cursed.
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</p>
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<h3>Schwarz H minimal surface (Triply periodic minimal surface)</h3>
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<figure>
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<img src='https://upload.wikimedia.org/wikipedia/commons/thumb/7/79/Schwarz_H_Surface.png/500px-Schwarz_H_Surface.png' width='500' height='480' />
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<figcaption>Image credit: <a href='https://commons.wikimedia.org/wiki/File:Schwarz_H_Surface.png#Licensing' target='_blank'>Anders Sandberg</a></figcaption>
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</figure>
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<p>
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Topology really takes the cake for making awful shapes no one ever wanted to look at.
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I’m not even sure what goes where here.
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With the normal geometry stuff, I could at least follow a general idea of what the shape was supposed to be.
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Now I feel like the shapes are mocking me.
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Wish I could provide more detail on the math here, but I’m out of my depth.
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</p><p>
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I could include many more horrible shapes here, but it’s getting late.
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I’ve already spent way more time on this post than I should have.
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So get ready, because here comes my pick for <i><b>the</b></i> worst shape ever:
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</p>
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<h2>Worst Shape Ever</h2>
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<h3>Alexander horned sphere</h3>
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<figure>
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<img src='https://upload.wikimedia.org/wikipedia/commons/thumb/0/0a/Alexander_horned_sphere.png/640px-Alexander_horned_sphere.png' width='640' height='480' />
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<figcaption>No one deserves credit for this abomination. (just kidding, the image is uncertainly attributed to a user named BernardH but it’s public domain)</figcaption>
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</figure>
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<p>
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Just look at that. Simply criminal. Even by mathematicians, this shape is considered pathological.
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</p><p>
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The pattern you see here goes on forever.
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To keep making this disaster of a shape, you have to keep removing sections and replacing it with a recursive pattern, forever.
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An ouroborous, twisting back to bite its own tail but never reaching, gnashing its teeth and fading away.
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</p><p>
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Once again, we have topologists to blame for this one, namely James Waddell Alexander II.
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I bet he’s proud of this nonsense.
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The really galling thing about it is that topologically, this thing is equivalent to a sphere.
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The friendly, puffy shape we all know and love, and this wicked, wicked shape claims relation to it.
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Truly the height of hubris (or perhaps the supremum of hubris for you depraved topologists).
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</p><p>
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Do you know of any other awful shapes?
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Have you seen a worse shape than the Alexander horned sphere? (not likely)
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Do you know of any wholesome shapes that may help me recover from this dark path I’ve lost myself on?
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Let me know your thoughts at my Ctrl-C email: <code>gome<span style='user-select: none;'> ​</span>@<span style='user-select: none;'> ​</span>ctrl-c.club</code>.
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</p>
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</article>
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</main>
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</body>
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</html>
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