# A Mandala Centered on a Regular Dodecagon

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.

# 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.

# 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.

# A Mandala Made of Hexagons, Enneagons, and Dodecagons

I recently re-discovered this “lost work,” which I made using Geometer’s Sketchpad, in 2011 — before I started this blog, which is why it has not appeared here before.