I previously blogged a different version of this symmetrohedron, one which sacrifices octagon regularity for regularity of all the other faces. Both polyhedra were created using Stella 4d: Polyhedron Navigator, which you can try for free right here. In this version, the twenty red hexagons are equiangular, and the sixty green faces are isosceles trapezoids.
This is the rhombic enneacontahedron, one of the few well-known zonohedra. Its ninety faces have two types: sixty wide rhombi, and thirty narrow rhombi.
In the image above, the thirty narrow rhombi of the rhombic enneacontahedron have been augmented with prisms.
The next step in today’s polyhedral play was to create the convex hull of this augmented rhombic enneacontahedron. This produced the solid shown immediately above. To make the one shown below, I next used a function called “try to make faces regular.” The result is a symmetrohedron with 122 faces: 12 regular pentagons, 30 rhombi, 60 almost-square isosceles trapezoids, and thirty equilateral triangles.
Finally, I examined the dual of this symmetrohedron, which turned out to have 120 faces: two sets of sixty kites each.
The program I used to create these polyhedral images is called Stella 4d, and you can try it yourself (as a free trial download) at http://www.software3d.com/Stella.php.
All of the edges of this polyhedron have the same length. I made it using Stella 4d: Polyhedron Navigator, which you can try for free at this website.
All of the edges of this polyhedron have the same length. I made it using Stella 4d: Polyhedron Navigator, which you can try for free at this website.
Stella 4d: Polyhedron Navigator has a “put models on vertices” function which I used to build this cluster of 61 icosahedra. If you’d like to try this software for yourself, there is a free trial download available at http://www.software3d.com/Stella.php.
Stella 4d: Polyhedron Navigator has a “put models on vertices” function which I used to build this cluster of cubes. If you’d like to try this software for yourself, there is a free trial download available at http://www.software3d.com/Stella.php.
Stella 4d: Polyhedron Navigator has a “put models on vertices” function which I used to build this cluster of 101 dodecahedra. If you’d like to try this software for yourself, there is a free trial download available at http://www.software3d.com/Stella.php.
Stella 4d: Polyhedron Navigator has a “put models on vertices” function which I used to build this complex of octahedra. If you’d like to try this software for yourself, there is a free trial version available at http://www.software3d.com/Stella.php.
Stella 4d: Polyhedron Navigator has a “put models on vertices” function which I used to build this complex of tetrahedra. If you’d like to try this software for yourself, there is a free trial version available at http://www.software3d.com/Stella.php.
RobertLovesPi.net 