What sort of polarizer is this? I wanted to try to experiment with polarizers, trying the 3 polarizers 45 degrees from each other, and similar experiments. I ordered 10 sheets of the cheapest polarizing foil I could find on Aliexpress. The package arrived today and it's... weird.
In one orientation it behaves like normal polarizers: Two sheets in parallel are barely dimmer than a single sheet, but if I turn one of them 90 degrees, I'm getting near-opacity where they overlay.


But when I change the order - place the sheet that was on top under the one that was on the bottom (without flipping it), I'm getting surprising results:
Perpendicular, the common part is about 50% opaque. 

And placed in parallel, I'm getting colorful hues, patterns of stripes, especially vivid if one of the sheets is slightly bent.


What sort of polarizer is this? What happens to the light, so that it produces these colorful patterns?
 A: The effect documented here is almost certainly the result of birefringence in the plastic film that supports the polarizers, particularly when it is under stress.
Basically, most cheap polarizers on the market are made from a thin film of polarizing material which forms a coating on one of the sides of a thin plastic sheet. If you place the two polarizers with the polarizing-film sides facing each other, you'll just see the idealized textbook effect, but if you turn one (or both) of them around, then the light will need to cross some amount of plastic sheet before it gets to the second polarizer. 
Secondly, this plastic sheet can be birefringent, often with none of its optical axes matching the direction of the polarizing film's axis, and often with the details of the birefringence depending on the stress, i.e. on how the material is bent. If the plastic is birefringent, then this means that it will change the polarization state of the light in between the two polarizers, both rotating it and making it elliptical, and both of those changes will induce dark regions where they happen. Moreover, this rotation depends on the amount of birefrigent material encountered, and the degree to which it is birefringent (basically, on the added optical path length between the two polarizations), and if it is enough then it can cause multiple rotations about the Poincaré sphere, which is where the fringes come from.
And finally, because this depends on the added phase more than the added path length, under white-light illumination this effect will affect the different component wavelengths by different amounts, and more specifically with different fringe spacings, which is why you get coloured fringes.
For more on this effect, the key search term is stress-induced birefringence; an image search for that term shows plenty of other examples. The obvious way to expand this is to introduce other plastic objects (say, a plastic fork) between the two polarizers, and the resulting fringes will bunch up at the places where the stress is concentrated.
