Tape Creations...

[BigV]

Originally Posted by glatt

Is that two different perspectives of one creation, or two different creations?

It looks like two different creations to me.

HM, have you ever considered stuff like Uniform Tilings when doing work like this? I do not understand the math behind practically all of that page, but I do recognize some of the illustrations from my imagination. I think of a dodecahedron, a regular polyhedron made up of triangular faces. Then, I see regular pentagons formed from your groups of five equilateral triangles and I wondered if those pentagons could be used to uniformly tile a sphere. And that's when I googlized wikipedia. I see triangles and pentagons and squares under your sub-units of triangles. It makes me wonder if you do all of this freestyle, just making a shape to connect to a previous shape, until you get to the last ones where you'd have to do some thinking, like a 3D game of Nim.

[Happy Monkey]

Originally Posted by BigV

It looks like two different creations to me.

HM, have you ever considered stuff like Uniform Tilings when doing work like this?

Not explicitly, though I assume that that type of math is involved when new polyhedra are discovered.

I think of a dodecahedron, a regular polyhedron made up of triangular faces. Then, I see regular pentagons formed from your groups of five equilateral triangles and I wondered if those pentagons could be used to uniformly tile a sphere.

Actually, a dodecahedron IS a pentagon-tiled sphere - 12 pentagons. The one with 20 triangles is an icosahedron.

It makes me wonder if you do all of this freestyle, just making a shape to connect to a previous shape, until you get to the last ones where you'd have to do some thinking, like a 3D game of Nim.

That most describes the process when I made this one (shown in progress):

Originally Posted by Happy Monkey

I made a corner, by making an icosahedron with 3 pentagons removed and replaced by rings of triangles. It looked like it might make something, so I made more corners until they met. The math isn't quite right, so as I got to the end, I had to use the flexibility of the material to pull it into shape, and certain interior parts look crushed.

There's another one I made by trial and error, which I'll post soon.

Usually, I have a polyhedron in mind from the web or a book, and I replace non-triangle faces with a pyramid made of triangles. That's how I made my favorite shape:



I found a polyhedron pattern, and replaced pentagons with concave pentagonal pyramids, and triangles with convex triangular pyramids, and it turned out that the faces of those lined up, creating diamond-shaped faces. And the resulting shape is actually the logo of Wolfram Alpha.