First, the heptagonal antiprism.
The rest of the polyhedra in this post were made from this antiprism, using the functions available in Stella 4d: Polyhedron Navigator, such as stellation and faceting. If you’d like to try this program yourself, you can do so, free, at http://www.software3d.com/Stella.php.
I turn 57 years old today, so here is a 57-pointed star to mark the occasion. It’s actually 3 stars, each of which has 19 points, which works because (3)(19) = 57. The individual stars here are {19/9} enneadecagrams — a blue one on the bottom layer, with green on the top, and red for the in-between star.
I’ve been making and blogging these birthday stars for well over a decade, and see no reason to stop any time soon. This one is made of four {7/3} heptagrams, shown in blue, with four {7/2} heptagrams shown in yellow. The area of intersection of these two types of star polygon is shown in green. This works to yield a 56-pointed star because (7)(4) + (7)(4) = 28 + 28 = 56.
This tessellation may be viewed in two different ways.
The first one is to see it as consisting of regular {12/5} dodecagrams, in orange, yellow, green, blue, and violet; along with rhombi in red; and equilateral triangles in magenta.
The second way is to view it as made of violet, regular dodecagons; kites, of four different sizes and shapes, in blue, green, yellow, and orange; red rhombi; and equilateral, magenta triangles.
Today is the day I turn 55, so here is a 55-pointed star to mark the ocassion. It’s composed of eleven five-pointed stars, which works because (5)(11) = 55.
In yesterday’s post, I unveiled my annual birthday star for my new age, 54. Today, I’m placing that 54-pointed star on each of the thirty faces of a rhombic triacontahedron. I use a program called Stella 4d (free trial available right here) to do this, and it allows images on polyhedron-faces to either be placed inside the face, or around the face. Here’s the “inside” version:
And here is the “around each face” version:
Which one do you like better?
I turn 54 years old today, so here is a 54-pointed star to mark the occasion. The nine repetitions of the six colors of the spectrum work because (6)(9) = 54.
These octagrams were rotated about the center point. Every other one is yellow, and between the yellow ones are blue ones. The green areas are where the blue and yellow octagrams coincide.
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