Actually, the most counterintuitive is 4-dimensional space. It is rather mathematically unique, often exhibiting properties no other dimension does.
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One of the most surprising is that all smooth manifolds of dimension not equal to four only have a finite number of unique smooth structures. For dimension four, there are countably infinite number of unique smooth structures. It's the only dimension with that property.
Though in a _very_ handwavy way it seems intuitive given properties like that in TFA where 4-d is the only dimension where the edges of the bounding cube and inner spheres match. Especially given that that property seems related to the possible neighborhoods of points in d-4 manifolds. Though I quickly get lost in the specifics of the maths on manifolds. :)
> However in four dimensions something very interesting happens. The radius of the inner sphere is exactly 1/2, which is just large enough for the inner sphere to touch the sides of the cube!