#stellated

This is the tetrahedrally-diminished dodecahedron, which can be formed from the Platonic dodecahedron by using faceting. In this case, I used Zometools. If you’d like to look into buying some Zome of your own, the website to visit is http://www.zometool.com. Stellating polyhedra is one of the things Zome was invented for. The two images below are two rotations of a stellated…

For that Kepler-Poinsot-Polyhedron I started to draw an icosahedron and continued to add triangular pyramids as "hats" on top of each of the 20 triangular icosahedron faces.

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This is the Small Stellated Dodecahedron I drew a while back:

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How are the Dodecahedron, Icosahedron, Small and Great Stellated Dodecahedron related?

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Truncation of the Small Stellated Dodecahedron:

Truncation of the Great Stellated Dodecahedron:

So I drew this dodecahedron and then the stellated dodecahedron below.

And when I drew that stellated dodecahedron I made some very annoying mistakes (in the last steps!)...

As I could not erase those ink lines, I improved and cut out the parts with mistakes...

Sadly, the cut outs are irritating for the perspective drawing. (I will show you why shading the faces will help make sense of this shape once I have made a second drawing of it.)

Now I cannot shade the stellated dodecehedron as it would look very messy with the cuts.

So I just use the stellated octahedron part as an interesting collage item.

I could even insert neon-colored paper, which would make it look fancy.

This is the thrid stellation of the rhombic dodecahedron. Its facelets are 24 rhombi and 24 “chevron” hexagons. Here’s another view, colored by individual face, with parallel faces having the same color. Finally, here’s one in “rainblow color mode.” I made these images using Stella 4d: Polyhedron Navigator, which you can try for free at http://www.software3d.com/Stella.php.

The Third Stellation of the Pentagonal Icositetrahedron Is a Compound of Two Irregular Dodecahedra

Here’s the pentagonal icositetrahedron. It is the dual of the snub cube.

And here is its third stellation. As you can see, it’s a compound of two irregular dodecahedra.

I made these images using Stella 4d: Polyhedron Navigator. You can try this program for free at http://www.software3d.com/Stella.php.