I stumbled upon these while playing with tetrahedral-symmetry alterations of a great rhombicuboctahedron, using Stella 4d. You can try this program for free at http://www.software3d.com/Stella.php.
This tessellation may be viewed in two different ways.
The first one is to see it as consisting of regular {12/5} dodecagrams, in orange, yellow, green, blue, and violet; along with rhombi in red; and equilateral triangles in magenta.
The second way is to view it as made of violet, regular dodecagons; kites, of four different sizes and shapes, in blue, green, yellow, and orange; red rhombi; and equilateral, magenta triangles.
In addition to the central dodecagon, this mandala has two rings of squares, one of equilateral triangles, a ring of rhombi, another of regular hexagons, and, finally, a ring of equilateral decagons.
This 110-faced polyhedron has, in addition to the eight regular dodecagons, six rectangles, and 96 triangles. I made it using Stella 4d, a program you can try for free, as a demo version, at http://www.software3d.com/Stella.php. I wish I could remember how I made it!
Fortunately, I have many friends who are more knowledgeable than I, when it comes to mathematics. Perhaps one of them will be able to solve this mystery.
Made with Stella 4d, available as a free trial download at http://www.software3d.com/Stella.php.
I made this polyhedron using Stella 4d,which you can try for free right here.
There are objects in hyperspace known as duoprisms, which have prismatic cells. This one’s cells are 24 dodecagonal prisms. It was made using Stella 4d, available here.
This is the truncated cube, one of the thirteen Archimedean solids.
If the truncation-planes are shifted, and increased in number, in just the right way, this variation is produced. Its purple faces are regular dodecagons, and the orange faces are kites — two dozen, in eight sets of three.
Applying yet another truncation, of a specific type, produces the next polyhedron. Here, the regular dodecagons are blue, and the red triangles are equilateral. The yellow triangles are isosceles, with a vertex angle of ~41.4 degrees.
All three of these images were produced using Stella 4d, available at this website.
Individual images may be enlarged with a click. They were created using Stella 4d: Polyhedron Navigator, which may be tried for free at http://www.software3d.com/Stella.php.
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