About RobertLovesPi

I go by RobertLovesPi on-line, and am interested in many things, a large portion of which are geometrical. Welcome to my little slice of the Internet. The viewpoints and opinions expressed on this website are my own. They should not be confused with the views of my employer, nor any other organization, nor institution, of any kind.

Twenty Hexagons, Each Adorned with Images of Hexagon the Cat

Hexagons

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.

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.