The Universe is actually flat

One working explanation for measurements of the CMBR says that it's a dodecahedron with its opposite faces touching. A ship traveling for long enough would eventually reach its starting point, but rotated (2*n)*36° along its movement axis.

So wouldn't everything inside a flat universe be flat as well? Well I feel stupid for doubting the Flat Earth Society.

EDIT: Or is it like the depiction of the documentary movies where 3D objects sit on a 2D plane that bends depending on the matter of the object?

Or maybe the Earth is a sphere, but it's on a flat plane.

When you say the universe is flat, are you only talking about it's shape, or about open-/flat-/closed-ness as well?

No, just no. What you are suggesting is that the Universe is two-dimensional. By "flat" universe, we mean that there is no curvature in it's shape, it says nothing about it's topology.

http://abyss.uoregon.edu/~js/cosmo/lectures/lec15.html

Right, flat usually corresponds to two-dimensional and the lecture seems to support the idea that the universe is a 2D plane(s).

the lecture seems to support the idea that the universe is a 2D plane

That's intended to be taken merely as an analogy. It's hard visualize bend 3D space.
"Flat" means "Euclidean" in this context. A flat space has, among others, the property that the angles of all triangles add up to 180° regardless of the size of the triangle. This is not true of bent space.

flat usually corresponds to two-dimensional

My table is flat, is it two-dimensional? Of course not. Flatness says nothing about topology. We still have no idea what the topology of the Universe is yet. Popular hypotheses include a dodecahedron (as helios mentioned), or a Mobius Strip (http://en.wikipedia.org/wiki/M%C3%B6bius_strip)

the lecture seems to support the idea that the universe is a 2D plane(s)

No, not a 2d plane, but flat like an *extremely large* piece of paper.

This was a link I shared in my original post, explaining why the Universe is known to be flat. Did you even read it?

http://map.gsfc.nasa.gov/universe/uni_shape.html

If you have peer reviewed research that supercedes Nasa, I would be glad to take a look at it.

I wasn't talking about it being 2D; maybe "flat plane" implies two dimensions but that's not what I meant. (Or were you talking to computerquip?).

Is there any evidence for whether the universe is open, closed or flat? Is the answer known? If not, what does the evidence most suggest?

I was talking to computerquip.

NASA and the WMAP saying the Universe is flat is the most compelling evidence we have to an answer.

EDIT:

If it isn't flat, the Universe is SO HUGE that it *appears* flat. But the observable Universe is only equal to it's age (as we know it), and is expanding faster than the speed of light...so who knows. I just stick to what the evidence suggests though, at least, until at least more information comes in.

I remember my cosmology lectures where we were working on a few scenarios for the future of the universe. One was a universe that would collapse upon itself, another was that the expansion rate would tend to zero then there was a case where the expansion rate increased exponentially. In the latter case after calculations if the rate kept on increasing would eventually rip the particles apart. I think maybe NOVA is referring to that theory.

Also the CMB radiation is really slow or something maybe because it is so cold close to 0 Kelvin so that we can map the state of the universe out and actually see in to its past.

flat usually corresponds to two-dimensional

Not in math talks. In math talks, the word "flat" corresponds to the vanishing of a tensor (which must explicitly be stated by the speaker: it can be Riemann-flat for the Riemannian metric, Ricci-flat for the Ricci curvature, etc.). In other words, the word "flat" means different things when used in different contexts, and all such contexts correspond to complicated formulas.

The origin of the word "flat" is that when similar formulas are used to describe two dimensional surfaces, certain tensor vanishings imply that the surface is in fact flat in the English sense of the word (piece of a plane).

When applied to our three dimensional world, the best way to understand the mathematical word "flat" is to look at the formulas in detail. In other words, all non-formula talk about 3-dimensional flatness is to attract positive publicity to scientific programs with strained budgets.