This is a frequency-4 geodesic icosahedron, made by request using *Stella 4d*, which you can try for yourself, free, at this website.

# Category Archives: Mathematics

# 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.

# 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.

# A Dodecahedron Made of Lux Blox . . . or Is It a Rhombicosidodecahedron?

This is the third polyhedral model I’ve built with Lux Blox, and the first to use the Lux trigons (the black pieces) which were added to the Lux system in 2017. If you view this polyhedron as having orange pentagonal faces, white edges, and black vertices, it’s a dodecahedron. On the other hand, it can be seen as having orange pentagonal faces, white square faces, and black triangular faces, in which case this is a rhombicosidodecahedron.

Lots of us are stuck inside because of COVID-19, and a set of Lux Blox is the perfect tool (or toy, if you prefer) to avoid boredom while we wait this thing out. You can find Lux for sale at www.luxblox.com, and delivery is fast.