Twelve of the icosahedron’s twenty faces have been hidden from view, exposing the small stellated dodecahedron nestled inside the icosahedron, and giving the visible parts of the model pyritohedral symmetry.
I made this using Stella 4d, a program you can try for yourself at http://www.software3d.com/Stella.php.
I found this by further stellation of the polyhedra shown in the two posts right before this one, using a program called Stella 4d: Polyhedron Navigator. You can try Stella for free at http://www.software3d.com/Stella.php.
I made this, using Stella 4d (available here), by multiple stellation of the faceted great rhombicosidodecahedron shown in the post immediately before this one.
I made this using the faceting function within Stella 4d: Polyhedron Navigator. You can try this program for free at http://www.software3d.com/Stella.php.
I made this using Stella 4d: Polyhedron Navigator. This program is available as a free trial download at http://www.software3d.com/Stella.php.
This polyhedron has, as faces, a dozen regular pentagons, thirty rhombi, and sixty irregular heptagons. I made this using Stella 4d, which is available as a free trial download at http://www.software3d.com/Stella.php.
Made with Stella 4d, available as a free trial download at http://www.software3d.com/Stella.php.
This is the snub cube. It’s one of the thirteen Archimedean solids.
The first modification I made to this polyhedron was to stellate it once.
The next step was to augment each yellow face with a tall prism.
Next, I formed the convex hull of the above solid.
The software I use to manipulate polyhedra, Stella 4d, has a function called “try to make faces regular.” The last step of this short polyhedral journey was to use this function on the above convex hull.
If you would like to try Stella 4d for yourself, there is a free trial download available at http://www.software3d.com/Stella.php.
The polyhedron shown above is the snub dodecahedron, which is one of the Archimedean solids. The one shown below is its first stellation.
Next, each of the yellow faces was augmented with a tall prism.
The next step was to form the convex hull of the polyhedron above.
Finally, I used Stella 4d‘s “try to make faces regular” function on this convex hull. The result is below, and has 242 faces.
If you would like to try Stella 4d, the software I used to do all of this, simply visit http://www.software3d.com/Stella.php, and look for the free trial download.
Sometimes, when using Stella 4d (available here) to make various polyhedra, I lose track of how I got from wherever I started to the final step. That happened with this fractured version of an octahedron.
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