An Octahedron, Augmented with Eight Great Icosahedra

You can’t see the octahedron; it’s hidden at the center of the figure.

Octa augmented with great icosahedra

I used Stella 4d to make this. You can try that program for yourself at http://www.software3d.com.

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A Polyhedron Made of Pentagons, Hexagons, and Octagons

octagons, hexagons, and pentagons

I used software called Stella 4d: Polyhedron Navigator to make this shape, and you can try Stella for free, right here. Sometimes, I use a lot of polyhedral modifications with this program, simply looking for a solid which looks interesting. With some polyhedra found through this random-walk process, I can’t even remember exactly how I created them in the first place — and this is one of those times.

I do know that this polyhedron has cuboctahedral symmetry, also known as octahedral symmetry. If  anyone can figure out more about it, especially how to construct it, you are invited to share your insights in a comment.

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A Zonohedron Featuring Hexadecagons

Zonohedrified Trunc Octa v e f.gif

I stumbled upon this zonohedron by adding zones to a truncated octahedron, based on its faces, edges, and vertices. It was created using Stella 4d, which you may try for free at http://www.software3d.com/Stella.php. To the best of my recollection, this is the only zonohedron I have seen which includes rhombi, hexagons, octagons, and, of course, the red hexadecagons.

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“What’s Your Favorite Color?”

I’ve been asked this question at least a hundred times. The answer is that my favorite color is black. 

black block

Black has been my favorite color for decades. As a college freshman, I even kept a black posterboard up on the wall, in my room at the dorm. Also, I don’t think I have ever been afraid of the dark. I actually find darkness comforting.

I usually get a protest, as a response, when I give my simple answer to this question: “Black’s not a color!”

At that point, nearly every time, I can end debate with a single question to my inquisitor: “What color is your t-shirt?” Sometimes they even look down at their shirt when I say this, and here’s what they typically see:

black t-shirt

I have no explanation for why the people who ask me to identify my favorite color are usually wearing black, but at least it quickly ends the conversation.

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“Spiders Aren’t Animals!” Well, Actually….

spider 240px-Kaldari_Phidippus_audax_01

Over the years, literally hundreds of people have told me that spiders are not animals. This seems to happen the majority of the times that the topic of spiders comes up in conversation.  When I reply that spiders are, in fact, animals, the usual response is “Spiders are insects!” This gives me headaches, because (1) spiders aren’t insects, and (2) insects are also animals.

Spiders happen to be my favorite animal, so this is quite confusing to me. Hopefully, this screenshot from my Google-search for “animal definition” will help spread the word that spiders are, indeed, part of the animal kingdom.

animals

[Spider image from https://en.wikipedia.org/wiki/Phidippus_audax. Also, I added the red arrow and ellipse to the Google-screenshot, using MS-Paint.]

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An Icosahedron Augmented with Twenty Great Icosahedra, together with the Dual of this Cluster-Polyhedron

icosa Augmented by great Icosas.gif

The cluster-polyhedron above was formed by augmenting a central isocahedron with twenty great icosahedra. The dual of this cluster is shown below.

icosa Augmented by great Icosas dual.gif

Both these images were created using Stella 4d, which you may try for free at http://www.software3d.com/Stella.php.

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A Flashing Mandala

flashing mandala

Mandalas are used for meditation and contemplation. They are also supposed to represent the universe, which we now know is in a constant state of change. Generally, this means mandalas are non-moving images, and (traditionally) they certainly don’t flash. This is, therefore, an attempt to update the concept of the mandala for the modern age, reflecting our current understanding of the universe.

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