Tag Archives: six

At 47, My Age Is a Prime Number Again =D

Posted on by
6

For some reason, I like having my age be a prime number of years. Today, I turn 47, so I get to have a prime-number-age for a whole year now. This hasn’t happened since I was 43, so I made this 47-pointed star to celebrate:

47

I also make birthday-stars for composite-number ages as well, just because it’s fun, and you can find at least two others on this blog, on January 12, in past years. Also, I wouldn’t want to have to wait until I’m 53 (my next prime age) to make another one of these.

At the moment, I certainly don’t feel 47. There are times when I feel twenty-two . . .

There are also times when I feel six.

calvin-on-learning

At the moment, however, I feel about thirty. For that reason, I put the 47-pointed stars on the thirty faces of a rotating rhombic triacontahedron, because (a) it’s my birthday, (b) I want to, and (c) I can.

Rhombic Triaconta

Image/music credits:

  1. I created this using Geometer’s Sketchpad and MS-Paint.
  2. “When Yer Twenty-Two,” by The Flaming Lips, via a YouTube posting.
  3. Two panels from a Calvin and Hobbes cartoon, by Bill Watterson. (Calvin is perpetually six years old.)
  4. Created using the image at the top of this post, and the program Stella 4d: Polyhedron Navigator, which is available here.

Two Compounds of Six Tetrahedra Each

Posted on by
Reply

compound of six elongated tetrahedra

In the image above, which I stumbled upon using Stella 4d (available here), the tetrahedra are elongated. If they are regular, instead, the same arrangement looks very different:

Tetrahedra 6

Six Pairs of Parallel Decagons

Image

Reply

Six Pairs of Parallel Decagons

Each pair is a different color. Because these decagons intersect in space, but do not meet at edges, they do not form a true polyhedron. They are merely a symmetrical configuration of twelve decagons in space, surrounding a central point.

I made this out a “true polyhedron” by hiding all the other faces from view. Before the hiding and recoloring of faces, this looked this way (you can click on it to enlarge it):

Augmented Convex hull

I used Stella 4d to make these images, and you can find that program at http://www.software3d.com/Stella.php.

The Compound of Six Dodecahedra

Image

Reply

The Compound of Six Dodecahedra

Some polyhedral compounds are well-known, such as the compound of five cubes, while others are less famous. I had never heard of this compound before building one today (virtually, not as a physical model). However, a quick Google-search told me that I was not the first person to discover it.

Software credit: see http://www.software3d.com/stella.php to try or buy Stella 4d, the software I used to create this image.