This can also be called the compound of two truncated tetrahedra.

This image was created using *Stella 4d*, which you can try at this website.

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This can also be called the compound of two truncated tetrahedra.

This image was created using *Stella 4d*, which you can try at this website.

This is the truncated dodecahedron. It is one of the Archimedean solids.

This polyhedron has a long stellation-series, from which I selected several on aesthetic grounds. The figure immediately below is the truncated dodecahedron’s 16th stellation.

Here is the 21st stellation.

It’s easy to stellate polyhedra rapidly, and make many other changes to them, with *Stella 4d: Polyhedron Navigator*. You can try it for free at http://www.software3d.com/Stella.php.

The stellation shown immediately above is the 25th, and the one shown immediately below is the 27th.

Here is the next stellation: the 28th. Unlike the ones shown above, it is chiral.

This is the truncated dodecahedron’s 31st stellation.

This one is the 38th stellation.

This one is the 44th.

The last one shown here is called the truncated dodecahedron’s final stellation because, if it is stellated once more, it returns to the original truncated dodecahedron.

I created these with *Stella 4d*, which you may try for free at this website. To make a given polyhedral stellation appear larger, simply click on it.

This is the truncated cube, one of the thirteen Archimedean solids.

If the truncation-planes are shifted, and increased in number, in just the right way, this variation is produced. Its purple faces are regular dodecagons, and the orange faces are kites — two dozen, in eight sets of three.

Applying yet another truncation, of a specific type, produces the next polyhedron. Here, the regular dodecagons are blue, and the red triangles are equilateral. The yellow triangles are isosceles, with a vertex angle of ~41.4 degrees.

All three of these images were produced using *Stella 4d*, available at this website.

This polyhedron has sixteen faces: four equilateral triangles, and a dozen kites. It was created using Stella 4d, which may be found at http://www.software3d.com/Stella.php.

I made this by faceting a truncated tetrahedron, giving it faces which are interpenetrating, red, equilateral triangles, as well as yellow crossed-edged hexagons. It can also be viewed as a central tetrahedron, with six more tetrahedra attached to its edges. This was made with *Stella 4d*, available at this website.

Each of these dodecahedra were modified by truncations at exactly four of their three-valent vertices. As a result, each has four equilateral triangles as faces. In the one above, the Platonic dodecahedron’s pentagonal faces are modified into a dozen irregular hexagons by these truncations, while, in the one below, the rhombic dodecahedron’s faces are modified into twelve irregular pentagons.

Both of these polyhedra were created using *Stella 4d*, software you can try for yourself at this website.

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