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.
Tag Archives: dodecagon
Dodecagonal Color Wheel with 30-60-90 Triangles
A Concave Polyhedron Featuring Eight Regular Dodecagons
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.
A Polyhedron Made of Regular Dodecagons and Kites
Made with Stella 4d, available as a free trial download at http://www.software3d.com/Stella.php.
A Polyhedron with 62 Faces Which Features Eight Regular Dodecagons
I made this polyhedron using Stella 4d,which you can try for free right here.
The Dodecagonal Duoprism
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.
The Truncated Cube, with Two Variations Featuring Regular Dodecagons
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.
Six Convex Polyhedra Featuring Convex Dodecagons, Some of Which Are Regular
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.
Two Convex Polyhedra with Tetrahedral Symmetry, Each Featuring Four Regular Dodecagons
The polyhedron above is a tetrahedrally-symmetric polyhedron featuring regular dodecagons and triangles, as well as two types of trapezoidal faces.
To make this second polyhedron from the first one, I first augmented each dodecagonal face with an antiprism, took the convex hull of the result, and then used the “try to make faces regular” function of the polyhedron-manipulation software I use, Stella 4d, which can be tried for free right here. The result is a polyhedron which maintains tetrahedral symmetry, and has, as faces, regular dodecagons and hexagons, as well as trapezoids and rectangles.