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.
The mandalas on the eight hexagonal faces of this truncated octahedron were first seen in the blog-post immediately before this one. The six square faces have been hidden, creating holes in their places.
I used Geometer’s Sketchpad and MS-Paint to make this pattern, based on a ring of twenty-two hendecagons. The work of projecting this image onto a polyhedron, as well as making this rotating .gif image, was performed using another program, Stella 4d: Polyhedron Navigator. If you’d like to try Stella for yourself, there’s a free trial download available at http://www.software3d.com/Stella.php.
These polyhedra are the rhombic dodecahedron (above), and the rhombic triacontahedron (below).
I made both of these using Stella 4d, which you can try for free at http://www.software3d.com/Stella.php. The tessellation on the faces of these polyhedra first appeared right here on this blog, in the post just before this one.
This is the icosidodecahedron. It’s one of the thirteen Archimedean solids. To make an expanded version of it, I first augmented each of its faces with a prism.
Next, I formed the augmented icosidodecahedron’s convex hull.
This expanded icosidodecahedron has the twelve pentagonal faces (shown in red) and twenty triangular faces (shown in blue) of the original icosidodechedron. It also has sixty rectangular faces (yellow), and sixty isosceles triangles (shown in green). That’s a total of 152 faces.