> If we take a vertical 2D slice of a tin can we get a rectangle.
> If we take a horizontal 2D slice of the same tin, we get a rectangle.
>
> So if we have a special shape that I will call a 4D Cylinder when taking
> 3d slices we can get a sphere or a block depending on which direction it
> is being sliced.

You can do it purely from a mathematical point of view if you feel like 
it - you can do isosurfaces right? :-)

3D:
A cylinder is x^2+y^2<1 and 0<z<1
If you fix z to 0.5 (your 2D plane) you get a circle.
If you fix x to 0 you get y^2<1 and 0<z<1 (ie a rectangle)

4D:
Try something like x^2+y^2+z^2<1 and 0<w<1
If you fix w=0.5 (your hyper-plane) you get a sphere
If you fix z=0 you get x^2+y^2<1 and 0<w<1 (ie a cylinder)

Or how about x^2+y^2<1 and 0<z<1 and 0<w<1
z=0.5 gives a cylidner
y=0 gives a 3D block

So as clipka says, I don't think there is any 4D shape you can define 
that you can "hyper-slice" to get either a block or a sphere. But that 
isn't exactly a proof - feel free to experiment, look forward to your 
images in p.b.i :-)

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