A Rhombic Dodecahedron Featuring Rotating Pentagonal Mandalas

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A Rhombic Dodecahedron Featuring Rotating Pentagonal Mandalas

Geometer’s Sketchpad and MS-Paint were both used to make the images on the faces of this polyhedron, and then Stella 4d was used to put it all together and create this rotating image. Stella may be bought, and/or tried for free, at www.software3d.com/Stella.php.

A Pentagonal Mandala In Primary Colors

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A Pentagonal Mandala In Primary Colors

Thirty Flying Rhombi

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Sixty Flying Rhombi

I used Stella 4d to make this image, and you can find that program at http://www.software3d.com/Stella.php.

Thirty Flying Hexagons

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Sixty Flying Hexagons

When I tweet a link to this blog-post as @robertlovespi, it will likely be quickly retweeted by @hexagonbot, simply because of the term “hexagon” being included in the tweet. What I don’t understand: Why do other polygons not have bots of their own?

I used Stella 4d to make this image, and you can find that program at http://www.software3d.com/Stella.php.

More Starry Polyhedra

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More Starry Polyhedra

These were all derived in various ways from the polyhedra seen in the last two posts. The rest are smaller at first, but each can be enlarged with a single click of your mouse. Each of them has icosidodecahedral symmetry.

Augmented Convex hullstellated Convex hullstellated Convex hull 2Astellated Convex hull 3stellation of mod of Compound of enantiomorphic pairstellation of mod of Compound of enantiomorphic pair 2stellation of mod of Compound of enantiomorphic pair 3

I used Stella 4d to make these images, and you can find that program at http://www.software3d.com/Stella.php.

Vincent Van Gogh, on Death, Passion, and Boredom

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Vincent Van Gogh, On Death, Passion, and Boredom

A Gallery of Twenty-One Polyhedra with Icosidodecahedral Symmetry

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Multiple Variants of the Icosidodecahedron

Click on the smaller pictures, if you wish to enlarge them, one at a time.

convex hull of prismaugmented RTCConvex hull of prismaugmented strombic hexacontahedronConvex hull of reaugmented convex hull of augmented RTCConvex hull qConvex hull z dualConvex hull z

Those last two were duals of each other. The next two are as well.

300-faced dual of 362-faced expanded snub dodecahedron convex hull augmented with 3x prisms362-faced expanded snub dodecahedron convex hull augmented with 3x prismsDual of Convex hullID variant

These next two are duals, as are the pair that follows them.

variant on the SSDdual of variant of SSDpolyhedron xpolyhedron x dual

regularized convex hull of prism-augmented RTCtwisted Convex hullStellated rainbow thingConvex hull

I’ll finish with one more dual pair.

UnnamedUnnamed

All of these were made using Stella 4d:  Polyhedron Navigator, which is available at http://www.software3d.com/Stella.php.

Candy

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Candy

Medium: electrons and photons, arranged carefully using Stella 4d: Polyhedron Navigator, software I bought at http://www.software3d.com/Stella.php. There is a free trial download available at the same website.

Twenty Rotating Triskelions, Made of Kites

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Twenty Rotating Triskelions, Made of Kites

Created using Stella 4d, software available at http://www.software3d.com/Stella.php.

Twelve Rotating Images of Barred Spiral Galaxy NGC1300

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Twelve Rotating Images of Barred Spiral Galaxy NGC 1300

After using Google to find the image of this galaxy, I used software called Stella 4d (available at http://www.software3d.com/Stella.php) to project it onto the twelve pentagonal faces of an icosidodecahedron, and then hid the triangular faces, as well as the vertices and edges — and then set the galaxies to rotate on the faces, as well as around the axis of the polyhedron.