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October 27[edit]

Mathematics from a dream...[edit]

I had a dream with several pieces of Mathematics that I don't have any clue where to go with this.

First of all, of the 43,380 different nets for an icosahedron, which one(s) have the minimum convex covering?
Is the answer the same if instead of mapping the net of the icosahedron onto the Euclidean plane, it is being mapped onto an order-10 triangular tiling (10 equilateral triangles meet at each point) of the hyperbolic plane?
Lastly for that minimum convex covering of the net of the icosahedron of order-10 triangular plane, are there 20 triangles which aren't part of the original net which themselves make up a net for an icosahedron?

In my dream, 12 alien cylinders had landed on earth and had forcefields connecting them and the earth began to unfold in that way (the forcefields connecting the cylinders separated from each other so that going through the forcefields eventually took as long as going around the cylinders (and it went from there)Naraht (talk) 03:00, 27 October 2013 (UTC)[reply]