A “Bowtie” Polyhedron Featuring Regular Enneagons and Octagons

So far as I know, no one knows how many otherwise-regular convex “bowtie” polyhedra exist — that is, convex polyhedra whose only faces are regular polygons, and pairs of isosceles trapezoids in “bowtie” formation. With the aid of software called Stella 4d, which you can find at http://www.software3d.com/Stella.php, I do believe I’ve found another one which hasn’t been seen before.

To make it, I started with what is probably the most well-known near-miss to the Johnson Solids, this polyhedron featuring enneagons (nine-sided polygons; also called “nonagons”):

Ennea-faced Poly

I then augmented each enneagonal face with regular antiprisms, took the convex hull of the result, and then used Stella’s “try to make faces regular” function — and it worked, making the octagons regular, as well as the enneagons.

Update:  It turns out that this polyhedron has been seen before.  It’s at http://www.cgl.uwaterloo.ca/~csk/projects/symmetrohedra/ — and there are even more at http://www.cgl.uwaterloo.ca/~csk/papers/kaplan_hart_bridges2001.pdf. These include several more “bowtie” polyhedra found among what those researchers, Craig S. Kaplan and George W. Hart, call “symmetrohedra.” They call this particular polyhedron a “bowtie octahedron.”

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.
Image | This entry was posted in Mathematics and tagged , , , , , , . Bookmark the permalink.

3 Responses to A “Bowtie” Polyhedron Featuring Regular Enneagons and Octagons

  1. Dave Smith says:

    Nonagons and octagons – nice combination.

    Liked by 1 person

  2. Brian H. says:

    nice, eight enneagons in one, and
    four enneagons with four octagons in another.

    on the simplest one, the four pentaga with two bowties,
    can you find the closed form for the dihedrdal angles?


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