A Concave Polyhedron Featuring Eight Regular Dodecagons

110 faces 8 dodec 6 rectangles 96 triangles

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

tet variant featuring reg dodecagons and equits

The polyhedron above is a tetrahedrally-symmetric polyhedron featuring regular dodecagons and triangles, as well as two types of trapezoidal faces.

tet variant using reg dodecagons and hexagons

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

recreational math from 2011

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.