Software credit: see http://www.software3d.com/Stella.php.

# Daily Archives: 27 May 2014

## Nervous Icosahedron

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Perhaps it had too much caffeine?

Software credit: see http://www.software3d.com/Stella.php.

## Polyhedron Featuring Eighty Regular Hexacontagons in the Pattern of the Triangles of a Snub Dodecahedron

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To make this, I attached tall pyramids (by their vertices) to the centers of the triangular faces of a snub dodecahedron. These pyramids have bases which are regular polygons with sixty sides each. After that modification of a snub dodecahedron, I took the convex hull of the result.

Just like the snub dodecahedron upon which this is based, this polyhedron is chiral. For any chiral polyhedron, *Stella 4d* (the software I use to make most of the images on this blog) will allow you to quickly make a compound of the polyhedron and its mirror image. When I did that, I obtained this result.

*Stella 4d* may be tried and/or bought at www.software3d.com/Stella.php.

## Octahedron with Beveled Vertices

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As an eight-sided die, this would work better than the Platonic octahedron, for it would roll more smoothly.

Software credit: see http://www.software3d.com/Stella.php.

## Prismatic Versions of Part of a Tessellation Using Squares and 60-120-60-120 Rhombi

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Above, the apparent size of the tessellation-prism does not change. In the next image, though, I set the controls of *Stella 4d* (the program I use to make these images, which you can try at http://www.software3d.com/Stella.php) to fit the image tightly, separately, in each still frame, causing a “breathing” effect. (Click on it if you wish to see it enlarged.)

Next, I added two red rhombi, one at the top and one at the bottom, stellated the result many times, and made one final .gif image, leaving the “breathing” effect on.

## Two Hourglass Cubes

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There are two six-member sets of hourglasses in the near-cube above, each of which is made of four not-quite-coplanar faces. One set is green and blue, while the other is magenta and blue.

If the polyhedron above is stellated nine times, the hourglasses expand until they compose the entire polyhedron. (To enlarge it, simply click on it.)

Software credit: all images here were created using *Stella 4d*. You may try it for yourself as a free trial version, or purchase the fully-functioning version, at http://www.software3d.com/Stella.php.

## An Octahedral Lattice of Rhombic Triacontahedra, Vanishing By Fifths

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These rhombic triacontahedra (RTCs) are each colored with the symmetrical five-color scheme for that polyhedron. It causes each color to appear six times on each RTC, in positions such that, for a single RTC, a centered x, y, and z axis can penetrate the centers of all six same-color faces.

Since there are five colors, this virtual model may be removed in fifths. The first to go are the green rhombi. (Each of these may be enlarged with a click.)

The next to be removed are the yellow rhombi.

The red ones are next to go.

One more fifth vanishes, and only the blue faces are left.

Finally, they are removed as well, but with edges and vertices now shown for the first time, for, otherwise, you’d see nothing here.

Software credit: all images here were created using *Stella 4d: Polyhedron Navigator*, my favorite polyhedron-manipulation tool. You may try it for yourself as a free trial version, or purchase the fully-functioning version, at http://www.software3d.com/Stella.php.