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Description
On top: How a standard octahedron tesselates, creating more details as you move closer (the details currently remain when you move out; there are details so small that they cannot be seen at all in the picture!)

Below: What happens when you give the tesselation the wrong instructions, and it starts to fold around you as you approach. This was supposed to be a sphere. It quite noticeably is not spherical.

Description
On top: How a standard octahedron tesselates, creating more details as you move closer (the details currently remain when you move out; there are details so small that they cannot be seen at all in the picture!)

Below: What happens when you give the tesselation the wrong instructions, and it starts to fold around you as you approach. This was supposed to be a sphere. It quite noticeably is not spherical.