This is a continuation of the process shown in the last post here, but with a different coloring-scheme.
I made this using Stella 4d, which you can try for free at this website.
Space-Filling Octagonal Prisms and Great Rhombcuboctahedra
1
Tag Archives: filling
Three Archimedean Solids Which Fill Space Together: The Great Rhombcuboctahedron, the Truncated Tetrahedron, and the Truncated Cube
To start building this space-filling honeycomb of three Archimedean solids, I begin with a great rhombcuboctahedron. This polyhedron is also called the great rhombicuboctahedron, as well as the truncated cuboctahedron.
Next, I augment the hexagonal faces with truncated tetrahedra.
The next polyhedra to be added are truncated cubes.
Now it’s time for another layer of great rhombcuboctahedra.
Now more truncated tetrahedra are added.
Now it’s time for a few more great rhombcuboctahedra.
Next come more truncated cubes.
More great rhombcuboctahedra come next.
More augmentations using these three Archimedean solids can be continued, in this manner, indefinitely. The images above were created with Stella 4d: Polyhedron Navigator, a program you may try for yourself at http://www.software3d.com/Stella.php.
A Close-Packing of Space, Using Three Different Polyhedra
Image
This is like a tessellation, but in three dimensions, rather than two. The pattern can be repeated to fill all of space, using cubes (yellow), truncated octahedra (blue), and great rhombcuboctahedra, also known as truncated cuboctahedra (red).
Software credit: see www.software3d.com/stella.php to try or buy Stella 4d, the software I used to create this image.
RobertLovesPi.net 