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Tesselation of the Plane with Regular Hexagons, Squares, and Tetraconcave Equilateral Octagons, #2

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A Tessellation Made of Many Circles

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Hexagonal Tessellation of Semicircles

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My 2025 Birthday Star

I turn 57 years old today, so here is a 57-pointed star to mark the occasion. It’s actually 3 stars, each of which has 19 points, which works because (3)(19) = 57. The individual stars here are {19/9} heptacontagrams — a blue one on the bottom layer, with green on the top, and red for the in-between star.

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To WordPress: I'll do my own writing, and your A.I. can go take a virtual leap off the top of a virtual skyscraper!

You can’t tell it from the web-address here, but this is a WordPress blog, and I’ve recently run into a new problem here. The WP user interface here has started volunteering to write my blog-posts for me, using a $#@%ed A.I. Of this I am certain: I have no intention on ever having an A.I. write anything for me, and find the suggestion both insulting and offensive. If you like the writing here,…

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Two Symmetrohedra Which Each Feature Four Regular Enneagons

This symmetrohedron has the following faces: four regular enneagons, four equilateral triangles, and twelve isosceles triangles with vertex angles of 43.5686 degrees. Its net is shown below. If this polyhedron is stellated once, the result is another symmetrohedron — one with four enneagonal faces, as well as twelve kites. The angles in the kites are 116.762, 99.8348, 43.5686, and 99.8348…

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A Polyhedral Journey, Starting With the Truncated Tetrahedron

Here’s the truncated tetrahedron. It is the simplest of the Archimedean solids. I decided to “take a walk” with this polyhedron. First, I used Stella 4d (available here) to make the compound of this solid and its dual, the Catalan solid named the triakis tetrahedron. Next, also using Stella (as I’m doing throughout this polyhedral journey), I formed the convex hull of this polyhedron — a solid…

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Tessellation of Regular Hexagons, Convex Pentagons, and Kites

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Happy Perfect-Square New Year 2025

As I write this, the new year of 2025 has already come to parts of the world. It arrives here, where we’re on Chicago time, in about four and a half hours. This new year is the first perfect-square year since 1936, and there won’t be another one until 2116. Since 45 = (9)(5) = (3^2)(5), and 2025 is the square of that, the prime number factorization of the new year is (3^4)(5^2). Happy New Year…

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The 35th Stellation of the Truncated Dodecahedron

I made this using Stella 4d: Polyhedron Navigator, which you can try for yourself, free, at http://www.software3d.com/Stella.php.

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Boycott Amazon -- Until the Strike is Resolved

Amazon workers are on strike against Amazon, for unfair labor practices, in multiple locations across the USA. While the strike continues, it is important that we support these workers and their unions, by doing these three things: Don’t buy anything from Amazon. Don’t buy Amazon’s stock. If you already own shares of Amazon, sell them. Since Amazon does most of its business on the Internet,…

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Thomas Jefferson Visits the Bagel Shop

I handed over payment, and the bagel shop guy said, “Um, I don’t know if we take these $2 bills….” The customer behind me laughed, and said just what I was thinking: “You have to take ’em, man — they’re legal tender!” Why do I get $2 bills from the bank at every opportunity? Because I live for moments like this, that’s why!

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Trump Apparently Skipped Out on Econ 101

Just when inflation was getting back to a reasonable level, we have this idiot, Trump, about to bring it back. Inflation ending doesn’t mean that prices go back to where they were — it merely means that prices stop climbing rapidly. If prices returned to, say, 2022 levels, that would be DEflation, which has its own set of problems we don’t want or need. The Great Depression was marked by…

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I'm Now an Official, Registered Tea Critic

I’ve been a coffee drinker since I was 19, but have recently acquired a taste for this particular tea, as well, which is shown in the picture above, which I “screenshotted” from Amazon. After guzzling it for several weeks, I decided to look up reviews of it, and found them at (where else?) http://www.teacritic.com. I then registered, at that website, so that I could add my own raving review. It’s…

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Hellos and Goodbyes. Goodbye, Facebook and X. Hello, BlueSky. If you're looking for me, read this post to find out where to find me on the Internet.

Like many people, I’ve lately become sick of so many things. It isn’t just Donald Trump and Trumpism, nor toxic forms of religion, nor anti-science attitudes, nor Elon Musk, nor the website X (formerly known as Twitter), nor Facebook, nor Mark Zuckerberg, nor billionaires in general, nor political parties, nor the war on women, nor anti-vaxxers, nor fascists on the far right, nor Communists on…

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My Advice for Voting in America in 2024

We are such a divided nation that I have to choose separate words for different types of Americans. Here goes…. To Harris supporters: vote, if you haven’t already! Donate to the campaign, if you can afford it! Give your neighbors rides to the polls! Call voters in swing states! To Trump supporters: Your vote is statistically insignificant. Whoever will win, will win, and there’s nothing you can…

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My Revised 2024 Election Prediction

I already posted one prediction-map for the 2024 presidential election, but that was back when Joe Biden was running for re-election. Since the Democratic candidate changed, I changed my prediction-map. If you want to create your own prediction-map, you can do so at http://www.270towin.com.