The Spidron is a planar figure consisting of two alternating sequences of isosceles triangles which, once it is folded along the edges, exhibits extraordinary spatial properties.
The Spidron can be used to construct various space-filling polyhedra and reliefs, while its deformations render it suitable for the construction of finely adjustable dynamic structures.
seems to demonstrate that it, at least in one iteration, begins with a
hexagon. Then equilateral triangles, several times into the center.
Then the basic shape is extrapolated out along edges, which involves vertices at the thirds points
on the way in and on the way out.
Blender subdivides, by default, in half.
Is there a way to adjust the subdivisions other than by half?
It would make it considerably easier to create the necessary break points
going in and to clean them up coming out.
Figured it out:
“Number of CutsSpecifies the number of cuts per edge to make. By default this is 1, cutting edges in half. A value of 2 will cut it into thirds, and so on.”
I used the method shown in the animated gif which begins with a hexagon and then drills down using equilateral triangles.
I think the result shown is consistent with his explanation.
I’m no mathematician.
Either what they did is consistent OR wrong.
I did what they did.
Their explanation:
“n geometry, a spidron is a continuous flat geometric figure composed entirely of triangles, where, for every pair of joining triangles, each has a leg of the other as one of its legs, and neither has any point inside the interior of the other. A deformed spidron is a three-dimensional figure sharing the other properties of a specific spidron, as if that spidron were drawn on paper, cut out in a single piece, and folded along a number of legs.”
- 