That’s the compound of the dodecahedron and the truncated octahedron above. Shown next is its dual, the compound of the icosahedron and the tetrakis cube. Both compounds were made using Stella 4d: Polyhedron Navigator, which you may try here.
Facetings are created by joining vertices to other vertices, but not choosing the vertices in the usual manner, which results in new positions for edges and faces. Faceting is also the reciprocal-function for polyhedral stellation. This is one of many possible facetings of the snub dodecahedron, and I created it using Stella 4d, which you can find here.
This faceting was created using Stella 4d, available here.
Created with Stella 4d, available here.
This is the first stellation of the second polyhedron seen in the post just before this one, but with the color-scheme changed, on the grounds that I like blue. If you’d like to know more about how this polyhedron was created, I refer you to that post. Stella 4d was used to make these: software you can try right here.
To make this, I used the excavation-function of Stella 4d, set to remove pyramids with equal edge length from each face of an icosidodecahedron. You can try this program here.
The dual of this polyhedron is shown below.
This is the familiar dodecahedron/icosahedron compound, but with each face of both components of the compound altered by the excavation of an equal-edge-length pyramid. To make it, as well as the rotating image below, I used Stella 4d, which you can find here.
Also, here is the dual of the compound above:
In this video, the great dodecahedron is stellated, by twentieths, into the great stellated dodecahedron, while a selection from Ludwig van Beethoven’s Ninth Symphony plays. The images for this video were created using Stella 4d, a program you can try for yourself (free trial download available), right here: http://www.software3d.com/Stella.php.
I made this with Stella 4d, software you can try here.
This compound was created using Stella 4d, software you can try for yourself here.
RobertLovesPi.net 