# Truncating the Rhombic Triacontahedron

This is the rhombic triacontahedron, one of the Catalan solids.

Now here’s the same polyhedron, but with the three-valent vertices truncated, exposing twenty triangular faces.

Here’s what it looks like with only the twelve five-valent vertices truncated.

Finally, here’s the fully truncated rhombic triacontahedron.

I created these polyhedra using Stella 4d, a program you can try for free right here.

# Truncating the Rhombic Dodecahedron

This is the rhombic dodecahedron, one of the Catalan solids.

Now here’s the same polyhedron, but with the three-valent vertices truncated, exposing eight triangular faces.

Here’s what it looks like with only the six four-valent vertices truncated.

Finally, here’s the fully truncated rhombic dodecahedron.

I created these polyhedra using Stella 4d, a program you can try for free right here.

## A Faceted Version of a Truncation of the Icosahedron

### Image

I made this with Stella 4d, a program you can find at http://www.software3d.com/Stella.php.

## The Truncated Truncated Icosahedron

### Image

The icosahedron has twenty triangular faces. Truncate it once, and the triangles become hexagons, with pentagons appearing under the pyramids removed in the truncation. This is the “soccer ball” shape familiar to millions.

If you take this figure and truncate it again, the twenty hexagons become twenty dodecagons, the twelve pentagons each become decagons, and sixty isosceles triangles appear under the pyramids removed by this second truncation.

I made this image using Stella 4d, a program you can find at www.software3d.com/Stella.php. Also, just for fun, here’s a version of it with the colors switched around, and with a slight bounce as it rotates in the other direction.