This is the rhombic dodecahedron, one of the Catalan solids.
Now here’s the same polyhedron, but with the three-valent vertices truncated, exposing eight triangular faces.
Here’s what it looks like with only the six four-valent vertices truncated.
Finally, here’s the fully truncated rhombic dodecahedron.
I created these polyhedra using Stella 4d, a program you can try for free right here.
I made this using Stella 4d, which you can find at this website.
This icosagon, with its diagonals showing, first appeared here. I then used Stella 4d to make the cube. You can try Stella for yourself at this website.
The 150 faces of this polyhedron include 30 convex octagons, as well as two sets of sixty elongated pentagons each. I made it using Stella 4d, which you can try for free at this website.
I made this using Stella 4d, which you can try for yourself at this website.
I made this using Stella 4d, which you can try for free at this website.
I made this compound using Stella 4d, which you may try for free at this website.
The first polyhedron shown here is also a symmetrohedron. 42 of its faces are regular decagons, and twenty are equilateral triangles. There are also sixty each of two types of isosceles trapezoids. That’s 182 faces in all.
The second polyhedron shown, below, also has 42 regular decagons as faces, along with twenty equiangular hexagons, sixty isosceles triangles, sixty almost-square isosceles trapezoids, and 120 of another kind of isosceles trapezoid. That’s a total of 302 faces.
The third one I found, shown below, has 42 decagons, sixty convex hexagons, twenty equilateral triangles, sixty rectangles, and sixty isosceles trapezoids, for a total of 242 faces.
I made all three of these polyhedra using Stella 4d: Polyhedron Navigator, which you can try for yourself, free, at http://www.software3d.com/Stella.php.
I made this using Stella 4d. If you’d like to try Stella yourself, the website to visit for a free trial download is http://www.software3d.com/Stella.php.
An icosagon is a twenty-sided polygon. Each segment-length was given its own color.
RobertLovesPi.net 