# Tag Archives: star

# My Birthday Star for 2020

This is the day I turn 52 years old, and I’m marking the occasion with a 52-pointed star. This particular star is a compound of four thirteen-pointed stars, each shown in a different color. This works because (4)(13) = 52.

# The 5/2, 5/2 Duoprism

I made this duoprism, a four-dimensional polytope, using *Stella 4d*. You can try this program for yourself, free, at http://www.software3d.com/Stella.php.

## Golden Star

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# Yellow Star Tessellation

In this tessellation, the hexagons, pentagons, and squares are all regular. The irregular polygons are equilateral decagons, as well as equilateral and concave tetrakaiicosagons.

## Tessellation of {8, 3} Star Octagons, and Two Sizes of Squares

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# My 2019 Birthday Star

I was born 51 years ago today. To mark the occasion, here’s a 51-pointed star. It’s made of {17/7} heptadecagrams repeated 3 times, and with their edges extended as lines, in three different colors. This works because 51 = (17)(3).

## Star Mandala

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# The Regular Enneagon, and Three Regular Enneagrams

The red figure above is a regular enneagon, or nine-sided polygon, and it has three regular enneagrams (or “star enneagons”) inside it. The light blue figure is called a {9,2} enneagram. The green figure can be viewed two ways: as a {9,3} enneagram, or as a compound of three equilateral triangles. Finally, the yellow figure is a {9,4} enneagram.

To see what these numbers in braces mean, just take a look at one of the yellow enneagram’s vertices, then follow one of the yellow segments to the next vertex it touches. Count the vertices which are skipped, and you’ll notice each yellow segment connects every fourth vertex, giving us the “4” in {9,4}. The “9” in {9,4} comes from the total number of vertices in this enneagram, as well as the total number of segments it has. The blue and green enneagrams are analogous to the yellow one. These pairs of numbers in braces are known as Schläfli symbols.

I should mention that some people call these figures “nonagons” and “nonagrams.” Both “ennea- and “nona-” refer to the number nine, but the latter prefix is derived from Latin, while the former is based on Greek. I prefer to use the Greek, since that is consistent with such Greek-derived words as “pentagon” and “hexagon.”

Finally, there is also an “enneagram of personality,” in popular culture, which some use for analyzing people. Aside from this mention of it, that figure is not addressed here — nor is the nine-pointed star used as a symbol for the Bahá’í faith. However, it’s easy to find information on those things with Google-searches, for those who are interested.