It’s made of rhombicosidodecahedra, and has the overall shape of a rhombicosidodecahedron as well. To make it, I started with the polyhedron in the last post, and then augmented each green pentagonal face with a rhombicosidodecahedron. I used software available here: http://www.software3d.com/stella.php.
To obtain this polyhedron, I took the one from the last post, and then augmented the twenty outermost triangles with icosidodecahedra. The fact that this new cluster has the overall shape of a dodecahedron caught be by surprise.
Software credit: see http://www.software3d.com/Stella.php for free trial download.
The polyhedral software I used to make this image may be purchased, or tried for free, at http://www.software3d.com/Stella.php.
An interference pattern / op art piece created with Geometer’s Sketchpad and MS-Paint.
This regular 4-d polytope is made of 600 tetrahedral unit cells. It is rotating in hyperspace, continually changing the three-dimensional “slice” of it which you can see. The software used to make this image may be purchased, or tried for free, at http://www.software3d.com/Stella.php.
(Note: I usually don’t post the writing of others, but learned that incorrect lyrics for this beautiful — and horrifying — song are all over the Internet. These are corrected, and if I have erred, even slightly, please correct me with a comment. This song is from the Lips’ new CD, The Terror, highly recommended in its entirety.)
Always there, in our hearts, fear of violence and of death
Always there, in our hearts, there is love and there is pain
Always there, in our hearts, there is evil that wants out
Always there, in our hearts, there are sorrows and sadness
Always there, in our hearts, never understanding
Always there, in our hearts, something pure that we can’t control
Can’t control, can’t control, can’t control
Always there, in our hearts, destroying everything we know
Always there, in our hearts, not forgiving them, who are we?
Always there, in our hearts, shame that we are all powerless
Always there, in our hearts, joy of life and overwhelmed
Overwhelmed, overwhelmed, overwhelmed, overwhelmed, overwhelmed
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Here is a music video for the song, also. The visual part of the video was created by Ben Maddox, and my source is his YouTube channel.
This is actually the mathematical dual of the previous post, but it reminds me of a butterfly, so I’m choosing to view it as closer to art than to mathematics.
Created with software available as a free trial download at http://www.software3d.com/stella.php.
The software used to make this is available as a free trial download at http://www.software3d.com/stella.php.
I made this .gif with Stella 4d, software available as a free trial download at http://www.software3d.com/stella.php.
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