This is a modification of the well-known tessellation of the plane with squares and regular octagons.
To make this zonohedron with Stella 4d (available as a free trial download here), start with a dodecahedron, and then perform a zonohedrification based on both faces and vertices. It is similar to the rhombic enneacontahedron, with thirty equilateral octagons replacing the thirty narrow rhombic faces of that polyhedron.
I’ve run into this polyhedron from time to time, and I’ve also had students make it. It is the largest zonohedron which can be built using only red and yellow Zome (available here). I thought it needed a name, so I made one up.
I’ve lost count of how many tessellations of octagons have appeared here. This might be the fifth one.
Several tessellations of octagons have been published in this space in the past. Here’s the latest in this occasional series.
I used Stella 4d: Polyhedron Navigator to make these. You can try it for yourself at http://www.software3d.com/Stella.php.
Unlike my previous octagon-tiling discoveries (see previous post), this is a chiral, radial tessellation, with the colors chosen to highlight that fact.
In April 2014, I found a tessellation of the plane which uses two kinds of octagons — both types equilateral, but only one type regular.
Now, I have found two more ways to tessellate a plane with octagons, and these octagons are also equilateral. However, in these new tessellations, only one type of octagon is used. One of them appears below, twice (the second time is with reversed colors), and the other one appears, once, in the next post.
To create the octagonal mandalas, I used Geometer’s Sketchpad and MS-Paint. I then projected them onto the faces of an all-but invisible dodecahedron, and created this rotating .gif image of it, using Stella 4d: Polyhedron Navigator, software you can try for free, right here.