Some Stellations of the Truncated Dodecahedron

The stellation-series of the truncated dodecahedron contains some interesting polyhedra. Selections from this series appear below.

24th Stellated Trunc Dodeca chiral

The polyhedron above is the 24th stellation of the truncated dodecahedron, while the one below is the 25th stellation.

25th stellation of Trunc Dodeca

27th Stellated Trunc Dodeca chiral

The polyhedron immediately above is the truncated dodecahedron’s 27th stellation. The one shown below is the 29th stellation.

29th Stellated Trunc Dodeca chiral

36th Stellated Trunc Dodeca chiral

The last two polyhedra in this post are the truncated dodecahedron’s 36th stellation (above), and its 70th stellation (below).

70th Stellated Trunc Dodeca

These images were created using Stella 4d, software available here.

 

The 21st and 22nd Stellations of the Truncated Dodecahedron

Stellation of a polyhedron involves extending its faces and/or edges into space to form other polyhedra, often with a star-like appearance, which is where the words “stellation,” “stellate,” and “stellated” originate. (“Stella” is Latin for “star.”)

Since this can be done repeatedly, long stellation-series exist for many polyhedra. In the case of the truncated dodecahedron, it was the 21st and 22nd stellations which I found the most aesthetically pleasing.

Here is the 21st stellation of this polyhedron:

Trunc Dodeca 21st stellation

And here is the 22nd:

Trunc Dodeca 22nd stellation

Both of these polyhedra were created with Stella 4d, software you may try for yourself, right here.

A Faceting of the Truncated Dodecahedron, Together with Its Dual

Faceted Trunc Dodeca

This faceting of the truncated dodecahedron, one of many, was made with Stella 4d, software you can buy, or try for free, here. Here is its dual, below.

dual of a faceted trunc dodeca

A Cluster of Truncated Dodecahedra

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A Cluster of Truncated Dodecahedra

I made this, using Stella 4d, by augmenting each decagonal face of the cluster in the previous post with a truncated dodecahedron. You can give this program a try yourself, for free, at http://www.software3d.com/stella.php.

A “Bowtie” Expansion of the Truncated Dodecahedron

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This polyhedron has the twelve regular decagons and twenty regular triangles of the truncated dodecahedron, but they are moved outwards from the center, and rotated slightly, creating gaps. These gaps are then filled with thirty pairs of isosceles trapezoids in “bowtie” formation. That gives this polyhedron 92 faces in all.

Software credit: see http://www.software3d.com/stella.php