You can crochet hyperbolic space, and prove non-euclidean geometry.
Number of straight lines through a point outside a line which do not touch the line:
0: sphere
1: Euclidean space
inf: hyperbolic space
Examples: the Klein bottle.
Also, thisperspective projection of a dodecahedral tessellation in H3.
Four dodecahedra meet at each edge, and eight meet at each vertex, just like a cubic tessellation in E3 (clipped from Wikipedia):
She gets there by crocheting a coral reef. Many animal have hyperbolic structure.
Conclusion: we need to create play-tanks, like think-tanks, which let one play with concrete forms of abstract ideas.
I'm in on the play tank! Also, I saw the crochet coral reef exhibit when it was at natural history museum here. It was stunning.
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