I have to say my friends the spiders were right.
They did say that reality was trochoidal in shape and composition, and they pointed out the plane in 3 straight lines. I half believe their N dimensional Hilbert/Hamiltonian spaces penchant.
Most do not like the octagonality of spiders, which is perhaps understandable when you are based on the factors 1,2,3,4,5,6, as our budy plan seems to be. Perhaps this is why we find greater affinity with the Bumble bee.
Nevertheless, the spiders have spoken and it seems to be true. A spider's web is an dimensional Hilbert space and it is flat. But this is a local perception.
thus space is macroscopically curved, locally flat and microscopically curved. Now this is a fractal stage description of reality, which is to say that this repeats itself at all scales ad infinitum!
We might have experienced this if we played around with the Nets for a solid geometry. We can draw nets for shapes up to the icosahedron, but we cannot use a plane figure in the net above a hexagon. If we do then the net tends to curve away in all directions. Klein played around with this and so can you.
Thus you can see the closed surface the plane surface and the curved surface all at different scales dependent on the geometry of the constituent faces/"spaces".
Imagine my spider friends kicking back with brightly coloured boots on enjoying a beer as they laugh at the wonder of the universe! There you go, you can see how hard they work to spin a web on one of the faces of reality!
Wouldn't you need 8 eyes to see what they see?