I tried to make a symmetrohedron using regular octadecagons and regular decagons, but that combination forces the octadecagons to overlap, and that causes the would-be symmetrohedron to be non-convex.
I tried to augment these octadecagons with antiprisms, and then form the convex hull of the result. Here’s what I found:
I made these using Stella 4d, which you can try for free right here.
The hexagons and squares in this polyhedron are regular; only the isosceles trapezoids are not. I made it using Stella 4d, which you can try for free right here.
This was a normal symmetrohedron, until I augmented its trapezoidal faces with pyramids. I did this using Stella 4d: Polyhedron Navigator, which you can try out for free at http://www.software3d.com/Stella.php.
I created this symmetrohedron as the zonohedron based on the faces, edges, and vertices of the tetrahedron. It has fifty faces: thirty squares, plus eight regular hexagons, and twelve merely-equilateral hexagons. I made it using Stella 4d, which you can try for free at this website.
I’ve spent a lot of time over the years looking for “near misses” to the Johnson Solids, and I’ve found two of them in all that time, starting in 2003. This isn’t one, for it has an edge length deviation of about 11%, which is too much to get overly excited about. It is, however, a symmetrohedron. The hexagons, pentagons, and yellow triangles are all regular; it’s only the blue triangles which are irregular (and isosceles). It has 122 faces in all. I think I can also say, with confidence, that it is a “near near miss.” In other words, it’s nearly a near-miss to the Johnson Solids. Confused yet? I know I am.
I made this using Stella 4d, software you can try for free at http://www.software3d.com/Stella.php.
I made this twenty-faced polyhedron using Stella 4d, which you can try for free at http://www.software3d.com/Stella.php.
I made this using Stella 4d, which you can try for free here.
I made this using Stella 4d. You can try this program for free at this website.
I made this using Stella 4d: Polyhedron Navigator. You can get a free trial download of this program at http://www.software3d.com/Stella.php.
This 38-faced polyhedron has been bugging me for over a week. I have a gut feeling that I’ve blogged it before, but my repeated searches have not found it. Perhaps I’m wrong, and it isn’t a “rerun” after all.
I made it using Stella 4d, which you can try for free at http://www.software3d.com/Stella.php.
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