Cuboctahedron Constructed from Rhombic Triacontahedra

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Cuboctahedron Constructed from Rhombic Triacontahedra

The software used to produce this image may be tried as a free trial download at http://www.software3d.com/Stella.php.

Mandala Based On 45

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Mandala Based On 45

Rotating Zonish Polyhedron

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Rotating Zonish Polyhedron

Creating zonish polyhedra (related to zonohedra) and creating rotating polyhedral .gifs are two features newly added to Stella, the program used to make this, which may be tried for free at http://www.software3d.com/stella.php

How To Age Slowly

This is the day I turn 45, and I still get carded when I buy beer. Those are my qualifications to write on this subject.

My first pieces of advice are to avoid tobacco altogether, and to moderate use of alcohol. I’ve seen people age prematurely, due to both factors, right in front of me (over a period of years), and it’s frightening. It’s also unnecessary, since these are both choices.

We also choose what we eat. My choices are limited by food allergies, though, forcing me lower on the food chain. I cannot eat mammals (nor shrimp) with becoming seriously ill, so I simply don’t eat beef, pork, etc. Perhaps this helps. It certainly cannot hurt.

Dysfunctional relationships make people unhappy, and unhappy people seem to age more quickly. I have found leaving bad relationships to be a most effective way of initiating (temporary, I hope) apparent reverse-aging, with the result that I look younger now than I did five or ten years ago.

I also feel younger. Are there aches and pains? Yes, there are, but they were worse at 35. I have chronic pain from a fall, and the resulting neck injury. Ten years ago, I was begging doctors for prescriptions for painkillers. Now, ibuprofen, stretching, and the occasional visit to my chiropractor give me the relief I need.

I think I would look 65 (or be dead) if I had not sought mental health treatment years ago, so getting such help, if you need it, is part of my advice. The problem here is often that people fear the stigma of mental illness, and delay seeking help, or avoid it altogether. Fighting back, to weaken that stigma, is the reason I write publicly on such subjects.

Another idea is a birthday ritual I have which, I must admit, can’t seriously be suggested as something that helps me age slowly, but it can’t hurt, either, and it’s fun. I make a star-design every year on my birthday, based on my new age. Here, therefore, is a star-design with 45 points:

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There is also an anti-aging attitude some people adopt, and I am one of them. This is a voluntary, deliberate refusal to stop being, in some senses (if not others), young. This can manifest itself in many ways; perhaps my star-ritual is one of them. Life is a game, of course, and I happen to like games — a lot.

Off-Center Mandala

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Off-Center Mandala

Snowflake in Primary Colors

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Snowflake in Primary Colors

Mandala Based on the Number 3

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Mandala Based on the Number 3

Golden Spectral Crystallization

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Golden Spectral Crystallization

Created using Geometer’s Sketchpad and MS-Paint.

A Polyhedral Journey

So I wondered, what would happen if I took rhombic dodecahedra…

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…and then affixed them to the sixty wider faces of a rhombic enneacontahedron?

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Well, it turns out that this is what you get:

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It’s at time like these — urgent situations in recreational mathematics — that I am most glad I bought Stella 4d, the program with which I made these images (and which you can try, for free, at http://www.software3d.com/stella.php). This would have taken months to figure out without the proper software! The next thing that occurred to me was to take the convex hull of the last polyhedron. That’s like draping a sheet around it and then pulling it tight. Here’s the result:

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Stella owes its name, in part, to a complex operation involving extensions of edges into lines, or faces into planes, called stellation. Stellating the above figure gave me something I didn’t like, but stellating it again gave me this:

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And then, after six more stellations, I arrived at the end of this particular polyhedral journey.

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Polyhedral Helix

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This helix is made of metabidiminished rhombicosidodecahedra, and was made using software you can try here.

Also, at this page on this blog, you can see a rotating version of a longer length of this same helix.