As promised, here are some pictures of the negative-curvature surface I made. (Thanks to my mom who made the pictures!)

(Click for larger.) As you can see, I ran out of blue yarn and continued with the light green, and I haven’t finished working on it. That’s a problem with a shape like this, in contrast to things like cubes or footballs: it doesn’t naturally stop somewhere…

The idea for this piece came from the tetrahedrons that I had made before. In a tetrahedron, in every corner three triangles meet. If you let four triangles meet at a corner, you get an octahedron – with eight faces. Five triangles meeting at a corner form part of an even larger structure, with twenty faces (five forming the top, five the bottom, and a strand of ten in between). Six regular triangles meeting at a corner might come as a disappointment: they fit into a flat circle, and no matter how many triangles you add, you’ll never get a closed surface.

So I decided to go a step further. The building block of this surface is a circle containing seven regular triangles, as you can see in more detail below the fold.

Since six regular triangles make up a circle, seven of those triangles do not fit into a flat circle: it has to bend into a saddle-shape to make room for them all. Because seven triangles meet at every corner of the surface, it’s easy to see that it has to have a saddle-shape – have negative curvature – everywhere.

Wow, you knit. You could teach at the “spinazie-academie” ;-)

Nicely done by the way. Although this picture might illustrate it too.

Did you read the title of the post? It’s crocheting (haken, in goed nederlands…), not knitting that I do.

I’ll consider the spinach-academy (?) in my quest for a new job….

Oh, I did miss that, sorry. It looked like knitting. I was refering to the old “huishoudschool” or “Lager Nijverhijds Onderwijs”.

I know…

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