The equiangular hexagons are very nearly regular, with only tiny deviations — probably not visible here — “from equilateralness.”
Little blurbs about posts on this blog get auto-tweeted on my Twitter, @RobertLovesPi. There’s also an A.I. on Twitter, @Hexagonbot, who retweeted my last two tweets about blog-posts here, but will not be retweeting the tweet about this one.
Why is this? Simple: @Hexagonbot is programmed to retweet any tweet which contains the word “hexagon,” which was in the titles of the last two posts here (also tessellations). This tessellation has no hexagons, though, and so the @Hexagonbot will not find it worthy of attention.
I cannot explain why hexagons get their own bot on Twitter, but other polygons do not have such bots. It’s simply one of the mysteries of the Internet.
Software credit: see http://www.software3d.com/stella.php
The faces of this polyhedron include:
12 decagons
30 octagons
60 light-colored hexagons
20 dark-colored hexagons
60 isosceles trapezoids
It was made with Stella 4d, software you can try and/or buy at http://www.software3d.com/stella.php.
This is the shape of the largest zonohedron one can make with red, yellow and blue Zome (see http://www.zometool.com for more on that product for 3-d real-world polyhedron modeling). This image was made using Stella 4d, which you can find at http://www.software3d.com/stella.php.
Created using software you can try at http://www.software3d.com/stella.php.
Later edit: I found this same polyhedron on another website, one that has been online longer than my blog, so I now for, for certain, that this was not an original discovery of my own. At http://www.cgl.uwaterloo.ca/~csk/projects/symmetrohedra/, it is named the “alternate bowtie dodecahedron” by Craig Kaplan and George W. Hart.
The 122 Faces are:
Created with Stella 4d, avaialable at http://www.software3d.com/stella.php.
RobertLovesPi.net 