This is a frequency-4 geodesic icosahedron, made by request using Stella 4d, which you can try for yourself, free, at this website.
By Request, A Geodesic Polyhedron
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Author Archives: RobertLovesPi
Twenty Hexagons, Each Adorned with Images of Hexagon the Cat
I made this using Stella 4d: Polyhedron Navigator, a program you can try for free at this website. It shows Hexagon the Cat riding in circles on the twenty hexagonal faces of a rotating truncated icosahedron. We don’t know of a cat named Pentagon, so I hid the twelve pentagonal faces.
Hexagon the Cat 1, Netflix 0
“Error Code M7353-5101” apparently means “We stopped playing Star Trek for you because your cat is sitting on the keyboard.” Hexagon strikes again!
A Cuboctahedron Made of Lux Blox
This cuboctahedron has an edge length of two. If you’d like to compare it to a Lux model with a edge length of one, just check the post right before this one. Lux Blox are fun to build with, and are sold online at http://www.luxblox.com.
A Truncated Icosahedron Made of Lux Blox
This particular truncated icosahedron has an edge length of one. I may build one with a longer edge length at some point; this would have the effect of shrinking the white edges, and magnifying the orange and blue faces, as fractions of the overall model. The individual Lux square pieces are identical, except for their color.
If you’d like to try Lux Blox for yourself, the site to visit is http://www.luxblox.com.
Improved Lux Octahedron
The first Lux Blox model I posted on this blog was an octahedron. After a little more practice, though, I have an improved model of this polyhedron to show here.
Lux are for sale at http://www.luxblox.com.
Expanding the Truncated Icosahedron, Using Augmentation with Prisms
Here’s my starting point: the truncated icosahedron, one of the thirteen Archimedean solids.
Next, each face is augmented by a prism, with squares used for the prisms’ lateral faces.
The convex hull of the polyhedron above yields what can be called an expanded truncated icosahedron, as shown below:
Could these faces be made regular, and the polyhedron still hold together? I checked, using Stella 4d‘s “try to make faces regular” function. Here’s the result:
As you can see, the faces of this polyhedron can be made to be regular, but this forces the model to become non-convex.
To try Stella for yourself, for free, just pay a visit to http://www.software3d.com/Stella.php. The trial version is a free download.
