The 43rd Stellation of the Snub Dodecahedron, and Related Polyhedra, Part Two

Just like I did in the first part of this two-part post, I’m starting with the snub dodecahedron’s 43rd stellation.

43rd stellation Snub Dodeca

This time, though, this polyhedral exploration is going in another direction. In the image below, the yellow kites seen above are shown augmented with prisms. The height of the prisms is equal to the average edge length of those kites.

Augmented Stellated Snub Dodeca

Creating the convex hull of this augmented polyhedron is the next step.

Cool polyhedron before TTMFR

The program I’m using to make these changes to polyhedra is called Stella 4d (it’s available here). The next step is using a function of Stella called “try to make faces regular.” The result is shown below.

242 faces 20 hex and 12 penta and 2x60 quads of two types and 30 quads of a third type and 60 triangles

Finally, I’m adjusting the coloring scheme so hexagons, pentagon, and triangles each get their own color, with a fourth color used for all three types of quadrilateral.

cool polyhedron colored by number of sides per face

Because I like this result, I’m stopping here.

About RobertLovesPi

I go by RobertLovesPi on-line, and am interested in many things. 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.

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