Quote - I'm learning this stuff myself, so don't have much to offer.

I like to figure out how things work by starting really simple.

I loaded a Poser box and a one-sided square. I rotated the square so it lays flat, and suspended it over the box. I enlarged it so that it's edges were outside the box. I then clothified the square and let it drop on the box.

It falls straight to the ground unless you start enabling some of those other collision detection options.

Further experiments led to some unexpected results.

A couple things I found out but don't really understand yet:

 1) The square folded in half, diagonally, to varying degrees for no reason. In the worst case, it folded up a lot.

The cloth simulation is based on vertices, not on polygons, so it really moves only the vertices of the cloth around, without caring too much if it actually forms a square. However, when moving the vertices around the square might get nonplanar, and has thus to be divided into two triangles. Note that a 3d renderer usually has a similar problem (nonplanar polygons), but it normally does not matter, since it is only interested in what is visible and what is not visible, so it can still maintain a continuous 4-sided polygon for shading etc. However for the cloth simulator, especially when polygon-collisions are enabled, The simple information on what is behind and what is in front is not enough, since the exact 3d-coordinates are needed. Hence the cloth-simulator really has to divide the n-sided polygons into triangles.

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2. When it landed on the box, quite often the preview showed serious poke through. But on rendering, there wasn't any.

I cannot say for sure, but the preview probably uses the triangulated mesh of the cloth-simulator, while the renderer (having more knowledge about where those triangles came from), can use the original (4-sided) polygons; i guess it does exactly that and renders the square and not the 2 triangles that were used to generate the deformation of the square.