Some might say the snub dodecahedron was twisted enough already, but I wanted to crank it up a notch, so I made this . . . using Stella 4d: Polyhedron Navigator, a program found at http://www.software3d.com/Stella.php.
In this virtual model, opposite planes have the same color. The beveling of the edges, this coloring method, plus the invisibility of certain parts, make the faces appear to be extensions of triangles, or triads of “v” shapes. Without this beveling effect on this coloring-method, however, it is easy to see that the true faces of this polyhedron are star pentagons. To see this second model enlarged — with this polyhedron’s traditional coloring — simply click on it.
The site to visit if you want to know how to make .gifs like these is http://www.software3d.com/stella.php.
Alternate names for components of this compound are the rhombicuboctahedron and the kited icositetrahedron.
For more information on the software used to produce this image, please visit http://www.software3d.com/stella.php.
Rhombic triacontahedra make quite versatile building-blocks for creating clusters in the shapes of other polyhedra. In this image (created with software you can find at http://www.software3d.com/Stella.php), a collection of them forms the overall shape of an octahedron.
Created with Stella 4d (site to try it: http://www.software3d.com/stella.php).
Created with Stella 4d (site to try it: http://www.software3d.com/stella.php).
Created with Stella 4d (site to try it: http://www.software3d.com/stella.php).
Created with Stella 4d (site to try it: http://www.software3d.com/stella.php).
This is the dual of the polyhedron from the previous post, although without any faces rendered invisible, as was the case with that one. I find it strongly reminiscent of the rhombic triacontahedron, but it has twice as many rhombi (sixty), as well as twenty triangles. Unlike the rhombic triacontahedron, this figure is chiral.
I can’t think of an appropriate name for this, so, if anyone has one, please leave your suggestion in a comment.
Created with Stella 4d (site to try it: http://www.software3d.com/stella.php).
One of the coolest things about the software I use to make these .gifs is the accidental discoveries. I didn’t even know this compound was possible until I stumbled upon it with Stella 4d. You can try this software at http://www.software3d.com/stella.php.
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