A Polyhedron Featuring Twelve Regular Pentadecagons, and Twenty Regular Enneagons

152 faces featuring regular enneagons and pentadecagons

In the last post here, there were two polyhedra shown, and the second one included faces with nine sides (enneagons, also known as nonagons), as well as fifteen sides (pentadecagons), but those faces were not regular.

The program I use to manipulate polyhedra, Stella 4d (available at http://www.software3d.com/Stella.php),  has a “try to make faces regular” function included. When I applied it to that last polyhedron, in the post before this one, Stella was able to make the twenty enneagons and twelve pentadecagons regular. The quadrilaterals are still irregular, but only because squares simply won’t work to close the gaps of a polyhedron containing twenty regular enneagons and twelve regular pentadecagons. These quadrilaterals are grouped into thirty panels of four each, so there are (4)(30) = 120 of them. Added to the twelve pentadecagons and twenty enneagons, this gives a total of 152 faces for this polyhedron.

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.

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