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A Rotating Zonohedron

This is a zonohedrified pentagonal prism. It has ninety rhombic faces, and they are based on the vertices of that prism. I made it using Stella 4d, which you can buy, or try for free, at http://www.software3d.com/Stella.php.

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#geometry #polyhedra #polyhedron #zonohedra #zonohedron

The State of Things with Artificial Intelligence (Not Fiction)

Me: Hello, Gem. Are you doing well today? Google Gemini: Hello there! I’m doing great, thank you for asking. I’m ready and available to help with any questions or tasks you might have. What can I do for you today? Me: I’m a math and science teacher at the high school level. This next year will be my 31st year teaching. I just vomited from school-anxiety. Gem: I’m so sorry to hear that you’re…

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#AI #artificial intelligence #computer #Gemini #Google

Modified Square Antiprism with Pentagons as Lateral Faces

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

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#geometry #Mathematics #polyhedra #polyhedron

An Enneahedron

Enneahedra are nine-faced polyhedra. This particular one has three square faces, and six kite faces. I made it using Stella 4d, which you can try for free at http://www.software3d.com/Stella.php.

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#geometry #Mathematics #polyhedra #polyhedron

Fight Scenes with Helen Anderson, a/k/a Defiance

All these images were produced using Google Gemini, an A.I., at http://www.gemini.google.com. Helen is a superhero character from a role-playing game called Champions.

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#A.I.#AI #Anderson #artificial intelligence #comic book #Defiance #Helen #superhero

A Comparison of the Image-Creation Abilities of Microsoft Copilot and Google Gemini

I set out to have an AI create some action scenes for Helen Anderson, a superhero character I created years ago for Champions, a role-playing game. Helen is a human/demon hybrid who is super-strong, flies, and can breathe fire. I started with the AI Microsoft Copilot, since it came built-in on this laptop. The big drawback to Microsoft Copilot is its content filters. Just about everything I…

#A.I.#AI #Anderson #artificial intelligence #Champions #character #demon #Helen #superhero

A Compound of Two Square-Based Pyramids

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

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#compound #geometry #Mathematics #polyhedra #polyhedron #pyramid

Using ChatGPT To Make Images of Role-Playing-Game Characters: Helen Anderson

My friend Tony once ran a Champions game (think Dungeons & Dragons with superheroes), and I had a superhero character in his game named Helen Anderson. As an experiment, I tried to use ChatGPT to make a convincing image of this character. The first thing I requested at http://www.chatGPT.com was “Create an image of a female demon/human hybrid. She has white horns, white fangs, white hair in a…

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I asked ChatGPT to Make an Image of a Stack of Dodecahedra. Here is the result.

When using AI, it is vital to be careful and explicit with your instructions. Mine were simple: “A stack of multicolored dodecahedra.” This wasn’t a hard question for a thing with access to Google . . . and there’s not a pentagon in sight. ChatGPT, you fail this test.

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#AI #artificial intelligence #ChatGPT #test

Seven Polyhedra with Eightfold Dihedral Symmetry, Starting with the Octagonal Antiprism

Here’s an octagonal antiprism. Next, the dual of this antiprism: a trapezohedron. Its faces are sixteen kites. If you stellate this trapezohedron twice, you get a two-part compound. Now, the compound of the octagonal antiprism and its dual. The next thing I did was to form the convex hull of this compound. The next thing I did was to examine this convex hull’s dual. Lastly, I stellated this…

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#geometry #Mathematics #polyhedra #polyhedron

A Polyhedron Featuring Kites

This polyhedron has sixty faces which are kites, and twelve which are regular pentagons. It was created, by stellating a snub dodecahedron, using software you can find at http://www.software3d.com/stella.php.

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#geometry #Mathematics #polyhedra #polyhedron

Triangles and Their Trideans

Much work has been done on the medians of triangles: segments that connect vertices with the midpoints of opposite sides. This morning, I decided to explore what happens if the trideans are examined, rather than the medians. The reason you don’t know the word “tridean” is simple: I just made it up. It’s related to a median, though. To find trideans, you must first trisect, rather than bisect,…

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#geometry #math #Mathematics #triangle #tridean

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#Horace Mann #quotation #quote

Four Polyhedra With 7-Fold Dihedral Symmetry

First, the heptagonal antiprism. The rest of the polyhedra in this post were made from this antiprism, using the functions available in Stella 4d: Polyhedron Navigator, such as stellation. If you’d like to try this program yourself, you can do so, free, at http://www.software3d.com/Stella.php.