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Foldable Snake Toys, of Two Sizes

This is the familiar “magic snake” toy which has been around for many years. The most common version of it is made of 24 right triangular prisms. It can be twisted into many different shapes. Of course, me being me, I wanted to make a polyhedron with it. Here are three of these standard-sized snake-toys, twisted into rhombicuboctahedra. While it isn’t easy, it is possible to find longer…

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Two Views of a Faceted Truncated Octahedron

In the image above, the faces of this faceted truncated octahedron are colored by face type. In the one below, the faces are colored by number of sides: blue for triangles, red for quadrilaterals, and yellow for hexagons. I made these using Stella 4d, which you can try for free at this website.

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A 32-Faced Symmetrohedron With Tetrahedral Symmetry

I made this polyhedron (using Stella 4d, which you can try for free here) by modifying the tetrated dodecahedron. Its 32 faces include four regular hexagons, twelve squares, four equilateral triangles, and twelve isosceles trapezoids.

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A Faceted Snub Cube, and Its Dual

The faceted snub cube shown above is colored by face type. The one below has faces colored by number of sides, with red triangles and yellow quadrilaterals. Here’s the dual of this particular faceting, shown in “rainbow color mode.” I made these virtual polyhedron models using Stella 4d, which you can try for free right here.

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On the Felon-in-Chief

Always remember: President Donald Trump is a convicted felon.

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Four Triangular Dipyramids, Surrounding a Common Point

I made this using multiple stellations, some of them with tetrahedral symmetry, to modify the cubohemioctahedron, one of the uniform polyhedra. I did this using Stella 4d, which you can try for yourself, free, at http://www.software3d.com/Stella.php. Also, here’s what the cubohemioctahedron looks like, without modification.

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A Second Tessellation Featuring Regular Octadecagons, Regular Octagons, Equiangular Hexagons, and Concave Pentagons

This is the same tessellation as the one in the last post, except that this one has had its colors inverted, using MS-Paint.

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Tessellation Featuring Regular Octadecagons, Regular Octagons, Equiangular Hexagons, and Non-Convex Pentagons

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A Purple-On-Purple Rendering of the Compound of Five Cubes

Here’s a link to the software I used to create this.

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A Red Great Icosahedron, Backed With More Red

I made this using Stella 4d, which you can try for free at this website.

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A Blue-On-Blue Rendering of the Final Stellation of the Icosahedron

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

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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…