What is the name of this triangular geometric shape?

[shintashi]

I used to think it was called Zeno's tower, but then realized I probably called it that because it reminded me of his paradox. I have been unable to find this shape on the internet, although I saw a small steel tower outside Stonybrook using this geometry.

I have attached an image of the basic structure and an animated gif in rotation to show how the angles look from different sides.

The pattern is equilateral triangles at 90 degrees to the edges, where a new triangle at 60 degree rotation forms the next level. This repeats to infinity, getting 4 times less surface area each floor. From some angles, its quite crude, and at other angles, its seamless.

Again, I have no idea if there is a name for this pattern, which has a kind of fractal quality when you zoom into the top.

 

[jedishrfu]

I think you’d call it an octehedral tower as each segment is an eight sided polyhedron ie an octahedron.

I found this related article of origami inspired designs

http://www.origamiheaven.com/macromodularorigami.htm

 

[shintashi]

I think you’d call it an octehedral tower as each segment is an eight sided polyhedron ie an octahedron.

I found this related article of origami inspired designs

http://www.origamiheaven.com/macromodularorigami.htm

it is true that it has some octagonal properties, but what's really interesting is how it expresses an X^2 expansion using a 3/6 side. There's an infinite number of surfaces, as you go further and further up, each is half the height and 1/4 the surface area of the previous. From the top, if you look through it, each distance expands exactly at the same ratio as light diffusion. This should be mathematically obvious, but I made one of these out of wood in 2007 and that's how i figured it out. The octahedral tower is nice but its linear, while this tower follows an exponential change creating a repeating simple fractal pattern. In a lot of ways, this tower is similar to three dimensional Sierpenski Triangle, but expands differently with saturation of increased triangles focused ever closer to the top, rather than equidistant.