A Cluster-Polyhedron Formed By 15 Truncated Octahedra, Plus Variations

15 Trunc Octa

To form the cluster-polyhedron above, I started with one truncated octahedron in the center, and then augmented each of its fourteen faces with another truncated octahedron. Since the truncated octahedron is a space-filling polyhedron, this cluster-polyhedron has no gaps, nor overlaps. The same cluster-polyhedron is below, but colored differently:  each set of parallel faces gets a color of its own.

15 Trunc Octa color by face unless parallel

This is the cluster-polyhedron’s sixth stellation, using the same coloring-scheme as in the last image:

15 Trunc Octa color by face unless parallel 6th stellation

Here’s the sixth stellation again, but with the coloring scheme that Stella 4d:  Polyhedron Navigator (the program I use to make these images) calls “color by face type.” If you’d like to try Stella for yourself, you can do so here.

15 Trunc Octa color by face type 6th stellation

Also colored by face-type, here are the 12th, 19th, and 86th stellations.

15 Trunc Octa color by face type 12th stellation

15 Trunc Octa color by face type 19th stellation

15 Trunc Octa color by face type 86th stellation

Leaving stellations now, and returning to the original cluster-polyhedron, here is its dual.

15 Trunc Octa dual

This image reveals little about this dual, however, for much of its structure is internal. So that this internal structure may be seen, here is the same polyhedron, but with only its edges visible.

15 Trunc Octa dual wirre-frame

Finally, here is an edge-rendering of the original cluster-polyhedron, but with vertices shown as well — just not the faces.

15 Trunc Octa wirre-frame

About RobertLovesPi

I go by RobertLovesPi on-line, and am interested in many things. The majority of these things are geometrical. Welcome to my little slice of the Internet. The viewpoints and opinions expressed on this website are my own. They should not be confused with the views of my employer, nor any other organization, nor institution, of any kind.
This entry was posted in Mathematics and tagged , , , , , , , , . Bookmark the permalink.

One Response to A Cluster-Polyhedron Formed By 15 Truncated Octahedra, Plus Variations

  1. teachezwell says:

    This one actually looks edible. Yum!

    Liked by 1 person

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s